Question 1

Which trigonometric identity is always true for any angle $A$?

Accepted Answer

Correct Option: D. Solution: All the given identities are standard trigonometric identities that hold true for all angles $A$ within their defined ranges.

Question 2

Prove the identity: $$\sec A (1 - \sin A)(\sec A + 	an A) = 1$$. Which of the following steps is necessary to simplify the left-hand side?

Accepted Answer

Correct Option: D. Solution: The identity $\sin^2 A + \cos^2 A = 1$ is used to simplify $1 - \sin^2 A$ to $\cos^2 A$, which is necessary for the simplification.

Question 3

Which trigonometric identity is not valid for $A = 90^\circ$?

Accepted Answer

Correct Option: B. Solution: The identity $1 + \tan^2 A = \sec^2 A$ is not valid for $A = 90^\circ$ because $\tan 90^\circ$ is undefined.

Question 4

In $	riangle ABC$, right-angled at $B$, if $\sin A = \frac{3}{5}$, what is the length of $BC$ if $AC = 10$ cm?

Accepted Answer

Correct Option: B. Solution: Since $\sin A = \frac{BC}{AC} = \frac{3}{5}$, and $AC = 10$ cm, $BC = \frac{3}{5} 	imes 10 = 6$ cm.

Question 5

In a right triangle $	riangle ABC$, right-angled at $B$, if $\sin A = \frac{3}{5}$, determine the value of $	an A$.

Accepted Answer

Correct Option: A. Solution: Given $\sin A = \frac{3}{5}$, which means the side opposite to angle $A$ is 3 and the hypotenuse is 5. Using the Pythagorean theorem, the adjacent side is $\sqrt{5^2 - 3^2} = \sqrt{25 - 9} = 4$. Therefore, $	an A = \frac{	ext{opposite}}{	ext{adjacent}} = \frac{3}{4}$.

Question 6

If $	an A = \frac{4}{3}$ in a right triangle, what is the length of the hypotenuse if the opposite side is $4k$?

Accepted Answer

Correct Option: A. Solution: Using the Pythagorean theorem, $	ext{hypotenuse}^2 = (4k)^2 + (3k)^2 = 25k^2$, so the hypotenuse is $5k$.

Question 7

In a right triangle $	riangle ABC$ with angle $A$ as an acute angle, which of the following identities is correct?

Accepted Answer

Correct Option: A. Solution: The identity $\sin^2 A + \cos^2 A = 1$ is a fundamental trigonometric identity valid for all angles $A$ in a right triangle.

Question 8

If $$\cos A = \frac{3}{5}$$, what is $$\sin A$$?

Accepted Answer

Correct Option: A. Solution: Using the identity $$\sin^2 A + \cos^2 A = 1$$, we find $$\sin A = \sqrt{1 - \left(\frac{3}{5}\right)^2} = \frac{4}{5}$$.

Question 9

Which trigonometric identity is represented by $$\sin^2 A + \cos^2 A = 1$$?

Accepted Answer

Correct Option: A. Solution: The identity $$\sin^2 A + \cos^2 A = 1$$ is known as the Pythagorean identity.

Question 10

If $	an A = \frac{1}{\sqrt{3}}$, what is the value of angle $A$?

Accepted Answer

Correct Option: A. Solution: The value of $	an A = \frac{1}{\sqrt{3}}$ corresponds to angle $A = 30^\circ$.

Question 11

In a right triangle $	riangle ABC$, right-angled at $B$, if $AB = 24$ cm and $BC = 7$ cm, what is the value of $\sin A$?

Accepted Answer

Correct Option: B. Solution: Using the Pythagorean theorem, $AC = \sqrt{AB^2 + BC^2} = \sqrt{24^2 + 7^2} = 25$ cm. Therefore, $\sin A = \frac{BC}{AC} = \frac{7}{25}$.

Question 12

If $$\sec A = 2$$, what is the value of $$\cos A$$?

Accepted Answer

Correct Option: A. Solution: Since $$\sec A = \frac{1}{\cos A}$$, then $$\cos A = \frac{1}{2}$$.

Question 13

For a right triangle $	riangle XYZ$, right-angled at $Y$, if $\cot Z = \frac{5}{12}$, what is the value of $\sec Z$?

Accepted Answer

Correct Option: B. Solution: Given $\cot Z = \frac{5}{12}$, let $YZ = 5k$ and $XY = 12k$. By Pythagoras theorem, $XZ = \sqrt{(5k)^2 + (12k)^2} = 13k$. Thus, $\sec Z = \frac{XZ}{XY} = \frac{13k}{12k} = \frac{13}{12}$.

Question 14

In the identity $$\sec A (1 - \sin A)(\sec A + 	an A) = 1$$, what is the role of $$\sec A$$?

Accepted Answer

Correct Option: A. Solution: $$\sec A$$ is the reciprocal of $$\cos A$$.

Question 15

In a right triangle $	riangle ABC$, if $\sec A = 2$, find $	an A$.

Accepted Answer

Correct Option: A. Solution: Given $\sec A = 2$, we have $\cos A = \frac{1}{2}$. Using $	an^2 A = \sec^2 A - 1$, we find $	an^2 A = 4 - 1 = 3$, hence $	an A = \sqrt{3}$.

Question 16

For a right triangle $	riangle ABC$, if $\cos A = \frac{3}{5}$, what is $	an A$?

Accepted Answer

Correct Option: A. Solution: Given $\cos A = \frac{AB}{AC} = \frac{3}{5}$, using $\sin^2 A + \cos^2 A = 1$, $\sin A = \frac{4}{5}$. Therefore, $	an A = \frac{\sin A}{\cos A} = \frac{4}{3}$.

Question 17

If $\sec A = 2$ and $0^\circ < A < 90^\circ$, what is the value of $	an A$?

Accepted Answer

Correct Option: A. Solution: Given $\sec A = 2$, we have $\cos A = \frac{1}{2}$. Using $	an^2 A = \sec^2 A - 1$, we find $	an^2 A = 4 - 1 = 3$, so $	an A = \sqrt{3}$.

Question 18

What is the value of $$	an 45^\circ$$?

Accepted Answer

Correct Option: B. Solution: In a right triangle with angles 45°, 45°, and 90°, the opposite and adjacent sides are equal, making $$	an 45^\circ = 1$$.

Question 19

If $	an A = \frac{3}{4}$ in a right triangle $	riangle ABC$, what is the value of $\sec A$?

Accepted Answer

Correct Option: A. Solution: Using the identity $1 + 	an^2 A = \sec^2 A$, we have $1 + \left(\frac{3}{4}ight)^2 = \sec^2 A$, which gives $\sec A = \frac{5}{4}$.

Question 20

In a right triangle, if one angle is 45°, what is the value of the hypotenuse if the length of each leg is $a$?

Accepted Answer

Correct Option: A. Solution: For a right triangle with angles 45°, 45°, and 90°, the hypotenuse is $a \sqrt{2}$ when each leg is $a$.

Question 21

In $	riangle PQR$, right-angled at $Q$, if $PQ = 3$ cm and $PR = 5$ cm, what is the value of $\sin R$?

Accepted Answer

Correct Option: A. Solution: In a right triangle, $\sin R = \frac{PQ}{PR} = \frac{3}{5}$.

Question 22

If $\sin A = \frac{1}{2}$ and $0^\circ < A < 90^\circ$, what is the value of $\cos A$?

Accepted Answer

Correct Option: A. Solution: Using the identity $\sin^2 A + \cos^2 A = 1$, we have $\cos^2 A = 1 - \left(\frac{1}{2}\right)^2 = \frac{3}{4}$. Thus, $\cos A = \frac{\sqrt{3}}{2}$.

Question 23

If $	an (A + B) = \sqrt{3}$ and $	an (A - B) = \frac{1}{\sqrt{3}}$, what are the values of $A$ and $B$?

Accepted Answer

Correct Option: A. Solution: Given $	an (A + B) = \sqrt{3}$ implies $A + B = 60^\circ$, and $	an (A - B) = \frac{1}{\sqrt{3}}$ implies $A - B = 30^\circ$. Solving these gives $A = 60^\circ$ and $B = 30^\circ$.

Question 24

What is the value of $$\sin 45^\circ$$?

Accepted Answer

Correct Option: A. Solution: The value of $$\sin 45^\circ$$ is $$\frac{1}{\sqrt{2}}$$ as derived from the properties of a 45°-45°-90° triangle.

Question 25

If $$	an A = \frac{4}{3}$$ in a right triangle, what is the length of the hypotenuse if the adjacent side is 3k?

Accepted Answer

Correct Option: A. Solution: Using the Pythagorean theorem, $$AC^2 = AB^2 + BC^2$$, where $$AB = 3k$$ and $$BC = 4k$$, we find $$AC = 5k$$.

Question 26

In a right triangle, if $\sin A = \frac{1}{3}$, what is the length of $AB$ if $BC = k$?

Accepted Answer

Correct Option: A. Solution: Given $\sin A = \frac{BC}{AC} = \frac{1}{3}$, so $AC = 3k$. Using the Pythagorean theorem, $AB = \sqrt{AC^2 - BC^2} = \sqrt{(3k)^2 - k^2} = 2\sqrt{2}k$.

Question 27

What is the value of $\sin 60^\circ$?

Accepted Answer

Correct Option: B. Solution: The value of $\sin 60^\circ$ is $\frac{\sqrt{3}}{2}$ as derived from the properties of a 30°-60°-90° triangle.

Question 28

In a right triangle, if $\cos A = \frac{1}{2}$, what is the measure of angle $A$?

Accepted Answer

Correct Option: C. Solution: The angle $A$ is $60^\circ$ because $\cos 60^\circ = \frac{1}{2}$.

Question 29

If $\sin A = \frac{1}{2}$, what is the possible value of angle $A$?

Accepted Answer

Correct Option: A. Solution: The value of $\sin A = \frac{1}{2}$ corresponds to angle $A = 30^\circ$.

Question 30

Given $$	an A = \frac{4}{3}$$ in a right triangle, find $$\sec A$$.

Accepted Answer

Correct Option: B. Solution: Using the identity $$\sec^2 A = 1 + 	an^2 A$$, we find $$\sec A = \sqrt{1 + \left(\frac{4}{3}ight)^2} = \frac{5}{3}$$.

Question 31

In a right triangle $	riangle ABC$, if $AB = 5$ cm, $BC = 4$ cm, and $\angle ABC = 90^\circ$, what is the length of $AC$?

Accepted Answer

Correct Option: D. Solution: Using the Pythagorean theorem, $AC = \sqrt{AB^2 + BC^2} = \sqrt{5^2 + 4^2} = \sqrt{25 + 16} = \sqrt{41}$ cm.

Question 32

Given $\sin A = \frac{1}{2}$, find $\cos A$ assuming $0^\circ < A < 90^\circ$.

Accepted Answer

Correct Option: A. Solution: Using $\sin^2 A + \cos^2 A = 1$, we have $\cos A = \sqrt{1 - \sin^2 A} = \sqrt{1 - \left(\frac{1}{2}\right)^2} = \frac{\sqrt{3}}{2}$.

Question 33

If $\tan A = \frac{1}{3}$, what is the value of $\sec A$?

Accepted Answer

Correct Option: A. Solution: Using the identity $\sec^2 A = 1 + \tan^2 A$, we find $\sec^2 A = 1 + \left(\frac{1}{3}\right)^2 = \frac{10}{9}$. Thus, $\sec A = \frac{\sqrt{10}}{3}$.

Question 34

If $\cot A = \sqrt{3}$, then what is $\cosec A$?

Accepted Answer

Correct Option: A. Solution: Given $\cot A = \sqrt{3}$, $\tan A = \frac{1}{\sqrt{3}}$. Using $1 + \cot^2 A = \cosec^2 A$, we find $\cosec^2 A = 1 + 3 = 4$, thus $\cosec A = 2$.

Question 35

If $$\sin A = \frac{1}{2}$$ in a right triangle, what is the length of the hypotenuse if the opposite side is 1 unit?

Accepted Answer

Correct Option: B. Solution: Since $$\sin A = \frac{	ext{opposite}}{	ext{hypotenuse}} = \frac{1}{2}$$, the hypotenuse is 2 units.

Question 36

In a right triangle $	riangle PQR$, right-angled at $Q$, if $PQ = 5$ cm and $PR = 13$ cm, find $\cos R$.

Accepted Answer

Correct Option: B. Solution: Using the Pythagorean theorem, $QR = \sqrt{PR^2 - PQ^2} = \sqrt{13^2 - 5^2} = 12$ cm. Thus, $\cos R = \frac{PQ}{PR} = \frac{12}{13}$.

Question 37

Which of the following trigonometric ratios is undefined for an angle of $90^\circ$?

Accepted Answer

Correct Option: C. Solution: The tangent of $90^\circ$ is undefined because it involves division by zero. In a right triangle, as the angle approaches $90^\circ$, the length of the side opposite the angle becomes equal to the hypotenuse, while the adjacent side approaches zero, leading to an undefined ratio.

Question 38

If $\cot A = \frac{3}{4}$, express $\sin A$ in terms of $\cot A$.

Accepted Answer

Correct Option: A. Solution: Given $\cot A = \frac{3}{4}$, we have $	an A = \frac{4}{3}$. Using $\sin^2 A + \cos^2 A = 1$ and $	an A = \frac{\sin A}{\cos A}$, we find $\sin A = \frac{4}{5}$.

Question 39

Which of the following trigonometric ratios is undefined?

Accepted Answer

Correct Option: A. Solution: $	an 90^\circ$ is undefined because the tangent function approaches infinity as the angle approaches $90^\circ$.

Question 40

In a right triangle, if $$\sin A = \frac{1}{3}$$, what is the length of the hypotenuse if the opposite side is k?

Accepted Answer

Correct Option: A. Solution: Since $$\sin A = \frac{	ext{opposite}}{	ext{hypotenuse}}$$, the hypotenuse is $$3k$$.

Question 41

If in a right triangle $	riangle ABC$, right-angled at $B$, $	an A = \frac{3}{4}$, what is the value of $\sin A$?

Accepted Answer

Correct Option: A. Solution: Given $	an A = \frac{3}{4}$, let $AB = 3k$ and $BC = 4k$. By Pythagoras theorem, $AC = \sqrt{(3k)^2 + (4k)^2} = 5k$. Thus, $\sin A = \frac{AB}{AC} = \frac{3k}{5k} = \frac{3}{5}$.

Question 42

Given $	an A = \frac{5}{12}$ in a right triangle $	riangle ABC$, right-angled at $B$, find $\sec A$.

Accepted Answer

Correct Option: A. Solution: Using the identity $\sec^2 A = 1 + 	an^2 A$, we have $\sec^2 A = 1 + \left(\frac{5}{12}ight)^2 = \frac{169}{144}$. Thus, $\sec A = \frac{13}{12}$.

Question 43

If $$\sin A = \frac{1}{3}$$ in a right triangle, which of the following is the correct expression for $$\cos A$$?

Accepted Answer

Correct Option: A. Solution: Using the identity $$\sin^2 A + \cos^2 A = 1$$, we have $$\cos A = \sqrt{1 - \sin^2 A} = \sqrt{1 - \left(\frac{1}{3}\right)^2}$$.

Question 44

Calculate $\cos 60^\circ$ using the properties of an equilateral triangle.

Accepted Answer

Correct Option: A. Solution: In an equilateral triangle, each angle is $60^\circ$. The cosine of $60^\circ$ is $\frac{1}{2}$.

Question 45

If $	an A = \frac{4}{3}$ in a right triangle, what is the length of the hypotenuse $AC$ if $BC = 4k$?

Accepted Answer

Correct Option: A. Solution: Given $	an A = \frac{BC}{AB} = \frac{4}{3}$, so $AB = 3k$. Using the Pythagorean theorem, $AC = \sqrt{AB^2 + BC^2} = \sqrt{(3k)^2 + (4k)^2} = 5k$.

Question 46

If in a right triangle $	riangle ABC$, right-angled at $B$, $\sin A = \frac{3}{5}$, express $\cos A$ in terms of $\sin A$.

Accepted Answer

Correct Option: B. Solution: Given $\sin A = \frac{3}{5}$, we use the identity $\sin^2 A + \cos^2 A = 1$. Therefore, $\cos^2 A = 1 - \sin^2 A = 1 - \left(\frac{3}{5}\right)^2 = \frac{16}{25}$. Thus, $\cos A = \frac{4}{5}$.

Question 47

The value of $	an 45^\circ$ is equal to 1.

Accepted Answer

Answer: True. Solution: For a right-angled triangle with angles $45^\circ$, $45^\circ$, and $90^\circ$, the ratio of the opposite side to the adjacent side is 1, hence $	an 45^\circ = 1$.

Question 48

The trigonometric ratio $	an 90^\circ$ is defined.

Accepted Answer

Answer: False. Solution: The tangent of $90^\circ$ is undefined because it involves division by zero, as $	an 	heta = \frac{	ext{opposite}}{	ext{adjacent}}$ and the adjacent side becomes zero at $90^\circ$.

Question 49

For any angle $A$, the identity $\sin^2 A + \cos^2 A = 1$ holds true.

Accepted Answer

Answer: True. Solution: This is a fundamental trigonometric identity that holds for all angles $A$. It is derived from the Pythagorean theorem.

Question 50

The value of $	an A$ is always less than 1 for all angles $A$.

Accepted Answer

Answer: False. Solution: The value of $	an A$ can be greater than, less than, or equal to 1 depending on the angle $A$. For example, $	an 45^\circ = 1$, but $	an 60^\circ = \sqrt{3}$, which is greater than 1.

Question 51

The value of $	an A$ is always less than 1 for any angle $A$ in a right triangle.

Accepted Answer

Answer: False. Solution: The value of $	an A$ can be greater than 1 depending on the angle $A$. For example, $	an 60^\circ = \sqrt{3}$, which is greater than 1.

Question 52

The trigonometric identity $\sin^2 A + \cos^2 A = 1$ is valid for all angles $A$ between $0^\circ$ and $90^\circ$.

Accepted Answer

Answer: True. Solution: The identity $\sin^2 A + \cos^2 A = 1$ is derived from the Pythagorean theorem and holds true for all angles $A$ in a right triangle.

Question 53

The value of $	an A$ is always less than 1 for all angles $A$.

Accepted Answer

Answer: False. Solution: The value of $	an A$ can be greater than 1 depending on the angle $A$. For example, $	an 60^\circ = \sqrt{3}$, which is greater than 1.

Question 54

The trigonometric ratio $\sin 45^\circ$ is equal to $\frac{1}{\sqrt{2}}$.

Accepted Answer

Answer: True. Solution: For a right triangle with angles 45°, 45°, and 90°, the sides are in the ratio 1:1:√2. Thus, $\sin 45^\circ = \frac{1}{\sqrt{2}}$.

Question 55

The trigonometric ratio $\sin 0^\circ$ is equal to 1.

Accepted Answer

Answer: False. Solution: The trigonometric ratio $\sin 0^\circ$ is defined as 0, not 1.

Question 56

The trigonometric ratio $\cos 90^\circ$ is 1.

Accepted Answer

Answer: False. Solution: As angle $A$ approaches 90°, the side adjacent to angle $A$ becomes nearly zero, making $\cos 90^\circ = 0$.

Question 57

The trigonometric ratio $\sec 90^\circ$ is not defined.

Accepted Answer

Answer: True. Solution: The value of $\sec 90^\circ$ is not defined because $\sec 	heta = \frac{1}{\cos 	heta}$ and $\cos 90^\circ = 0$, leading to division by zero.

Question 58

The equation $1 + 	an^2 A = \sec^2 A$ is not valid for $A = 90^\circ$.

Accepted Answer

Answer: True. Solution: The equation $1 + 	an^2 A = \sec^2 A$ is derived from dividing the Pythagorean identity by $\cos^2 A$. Since $	an A$ and $\sec A$ are not defined for $A = 90^\circ$, the equation is not valid at this angle.

Question 59

In a right triangle, if the angle $A$ is very close to $90^\circ$, the side $AC$ almost coincides with side $BC$, making $\cos A$ very close to zero.

Accepted Answer

Answer: True. Solution: As angle $A$ approaches $90^\circ$, the side $AC$ becomes nearly equal to $BC$, resulting in $\cos A$ approaching zero.

Question 60

The value of $\sin A$ or $\cos A$ can exceed 1 for some angles $A$.

Accepted Answer

Answer: False. Solution: In a right triangle, the hypotenuse is the longest side, so the values of $\sin A$ and $\cos A$, which are ratios involving the hypotenuse, are always less than or equal to 1.

Question 61

The trigonometric identity $\sin^2 A + \cos^2 A = 1$ is valid for all angles $A$ between $0^\circ$ and $90^\circ$.

Accepted Answer

Answer: True. Solution: The identity $\sin^2 A + \cos^2 A = 1$ is derived from the Pythagorean theorem and holds true for all angles $A$ in the range $0^\circ \leq A \leq 90^\circ$.

Question 62

The equation $\sec A (1 - \sin A)(\sec A + 	an A) = 1$ is a trigonometric identity valid for all angles $A$.

Accepted Answer

Answer: True. Solution: The equation is a trigonometric identity because it holds true for all values of angle $A$ within its domain. This can be proven by algebraic manipulation using known trigonometric identities.

Question 63

The value of $\sin A$ or $\cos A$ can exceed 1 in a right triangle.

Accepted Answer

Answer: False. Solution: The value of $\sin A$ or $\cos A$ never exceeds 1 in a right triangle, as these are ratios involving the hypotenuse, which is the longest side.

Question 64

The trigonometric identity $1 + \cot^2 A = \csc^2 A$ is not defined for $A = 0^\circ$.

Accepted Answer

Answer: True. Solution: The identity $1 + \cot^2 A = \csc^2 A$ involves $\cot A$ and $\csc A$, which are not defined for $A = 0^\circ$.

Introduction to Trigonome..

Learning Objectives

Learning Objectives

Revision Notes & Summary

Chapter Notes

Trigonometric Ratios and Identities

Trigonometric Ratios of Specific Angles

Trigonometric Ratios in Terms of Each Other

Applications of Trigonometric Ratios

Trigonometric Equations and Proofs

Exam Tips & Common Mistakes

Common Mistakes & Exam Tips

Trigonometric Ratios and Identities

Trigonometric Ratios of Specific Angles

Trigonometric Ratios in Terms of Each Other

Applications of Trigonometric Ratios

Trigonometric Equations and Proofs

General Tips

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Multiple Choice Questions

Q1.Which trigonometric identity is always true for any angle AAA?

Correct Answer: D

Q2.Prove the identity: sec⁡A(1−sin⁡A)(sec⁡A+tan⁡A)=1\sec A (1 - \sin A)(\sec A + \tan A) = 1secA(1−sinA)(secA+tanA)=1. Which of the following steps is necessary to simplify the left-hand side?

Correct Answer: D

Q3.Which trigonometric identity is not valid for A=90∘A = 90^\circA=90∘?

Correct Answer: B

Q4.In △ABC\triangle ABC△ABC, right-angled at BBB, if sin⁡A=35\sin A = \frac{3}{5}sinA=53​, what is the length of BCBCBC if AC=10AC = 10AC=10 cm?

Correct Answer: B

Q5.In a right triangle △ABC\triangle ABC△ABC, right-angled at BBB, if sin⁡A=35\sin A = \frac{3}{5}sinA=53​, determine the value of tan⁡A\tan AtanA.

Correct Answer: A

Q6.If tan⁡A=43\tan A = \frac{4}{3}tanA=34​ in a right triangle, what is the length of the hypotenuse if the opposite side is 4k4k4k?

Correct Answer: A

Q7.In a right triangle △ABC\triangle ABC△ABC with angle AAA as an acute angle, which of the following identities is correct?

Correct Answer: A

Q8.If cos⁡A=35\cos A = \frac{3}{5}cosA=53​, what is sin⁡A\sin AsinA?

Correct Answer: A

Q9.Which trigonometric identity is represented by sin⁡2A+cos⁡2A=1\sin^2 A + \cos^2 A = 1sin2A+cos2A=1?

Correct Answer: A

Q10.If tan⁡A=13\tan A = \frac{1}{\sqrt{3}}tanA=3​1​, what is the value of angle AAA?

Correct Answer: A

Q11.In a right triangle △ABC\triangle ABC△ABC, right-angled at BBB, if AB=24AB = 24AB=24 cm and BC=7BC = 7BC=7 cm, what is the value of sin⁡A\sin AsinA?

Correct Answer: B

Q12.If sec⁡A=2\sec A = 2secA=2, what is the value of cos⁡A\cos AcosA?

Correct Answer: A

Q13.For a right triangle △XYZ\triangle XYZ△XYZ, right-angled at YYY, if cot⁡Z=512\cot Z = \frac{5}{12}cotZ=125​, what is the value of sec⁡Z\sec ZsecZ?

Correct Answer: B

Q14.In the identity sec⁡A(1−sin⁡A)(sec⁡A+tan⁡A)=1\sec A (1 - \sin A)(\sec A + \tan A) = 1secA(1−sinA)(secA+tanA)=1, what is the role of sec⁡A\sec AsecA?

Correct Answer: A

Q15.In a right triangle △ABC\triangle ABC△ABC, if sec⁡A=2\sec A = 2secA=2, find tan⁡A\tan AtanA.

Correct Answer: A

Q16.For a right triangle △ABC\triangle ABC△ABC, if cos⁡A=35\cos A = \frac{3}{5}cosA=53​, what is tan⁡A\tan AtanA?

Correct Answer: A

Q17.If sec⁡A=2\sec A = 2secA=2 and 0∘<A<90∘0^\circ < A < 90^\circ0∘<A<90∘, what is the value of tan⁡A\tan AtanA?

Correct Answer: A

Q18.What is the value of tan⁡45∘\tan 45^\circtan45∘?

Correct Answer: B

Q19.If tan⁡A=34\tan A = \frac{3}{4}tanA=43​ in a right triangle △ABC\triangle ABC△ABC, what is the value of sec⁡A\sec AsecA?

Correct Answer: A

Q20.In a right triangle, if one angle is 45°, what is the value of the hypotenuse if the length of each leg is aaa?

Correct Answer: A

Q21.In △PQR\triangle PQR△PQR, right-angled at QQQ, if PQ=3PQ = 3PQ=3 cm and PR=5PR = 5PR=5 cm, what is the value of sin⁡R\sin RsinR?

Correct Answer: A

Q22.If sin⁡A=12\sin A = \frac{1}{2}sinA=21​ and 0∘<A<90∘0^\circ < A < 90^\circ0∘<A<90∘, what is the value of cos⁡A\cos AcosA?

Correct Answer: A

Q23.If tan⁡(A+B)=3\tan (A + B) = \sqrt{3}tan(A+B)=3​ and tan⁡(A−B)=13\tan (A - B) = \frac{1}{\sqrt{3}}tan(A−B)=3​1​, what are the values of AAA and BBB?

Correct Answer: A

Q24.What is the value of sin⁡45∘\sin 45^\circsin45∘?

Correct Answer: A

Q25.If tan⁡A=43\tan A = \frac{4}{3}tanA=34​ in a right triangle, what is the length of the hypotenuse if the adjacent side is 3k?

Correct Answer: A

Q26.In a right triangle, if sin⁡A=13\sin A = \frac{1}{3}sinA=31​, what is the length of ABABAB if BC=kBC = kBC=k?

Correct Answer: A

Q27.What is the value of sin⁡60∘\sin 60^\circsin60∘?

Correct Answer: B