Trigonometric Ratios & Identities PYQs - Last 10 Years

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Practice 31 COMEDK Mathematics questions from Trigonometric Ratios & Identities. Use the year-wise and type-wise breakdown to prioritize recent PYQs, then continue into the question list below.

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Mathematics / Trigonometry

2020-2026

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2022-2026

31

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2017-2026

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Last 10 Years Trigonometric Ratios & Identities Questions

Showing 31 of 31 filtered questions.

1Trigonometric Ratios And Identities

If $\sin A+\sin 2 A=x$ and $\cos A+\cos 2 A=y$ then the value of the expression $\left(x^2+y^2\right)\left(x^2+y^2-3\right)$ equals

2Trigonometric Ratios And Identities

\(\text { The expression } \frac{1-\tan ^2\left(\frac{\pi}{4}-A\right)}{1+\tan ^2\left(\frac{\pi}{4}-A\right)} \text { equals }\)

3Trigonometric Ratios And Identities

$$ \text { The expression } \frac{\tan \left(x-\frac{\pi}{2}\right) \cos \left(\frac{3 \pi}{2}+x\right)-\sin ^3\left(\frac{7 \pi}{2}-x\right)}{\cos \left(x-\frac{\pi}{2}\right) \tan \left(\frac{3 \pi}{2}+x\right)} \text { simplifies to: } $...

4Trigonometric Ratios And Identities

Suppose 'a' and 'b' are non-zero constants satisfying the following system of equations $\boldsymbol{a} \sin ^3 x+\boldsymbol{b} \cos ^3 x=\sin x \cos x$ and $\mathbf{a} \sin x-\boldsymbol{b} \cos x=0$, then $\mathbf{2}\left(\boldsymbol{a}^...

5Trigonometric Ratios And Identities

If $2 \sin \theta=\left(x+\frac{1}{x}\right)$, then $\sin 3 \theta+\frac{1}{2}\left(x^3+\frac{1}{x^3}\right)=$

6Trigonometric Ratios And Identities

If $\tan x^{\circ} \tan 2^{\circ} \tan 3^{\circ} \ldots \ldots \ldots \ldots . . \tan 88^{\circ} \tan y^{\circ}=1$ then $\cot (x+y)=$

7Trigonometric Ratios And Identities

If $\sin A+\sin B=-\frac{21}{65}, \cos A+\cos B=-\frac{27}{65}$ and $\pi

8Trigonometric Ratios And Identities

The value of $\frac{1}{2 \sin 10^{\circ}}-2 \sin 70^{\circ}$ is

9Trigonometric Ratios And Identities

The value of $\frac{\sin ^2 20^{\circ}+\cos ^4 20^{\circ}}{\sin ^4 20^{\circ}+\cos ^2 20^{\circ}}$ is :

10Trigonometric Ratios And Identities

If $\tan \alpha=\frac{1}{7}$ and $\sin \beta=\frac{1}{\sqrt{10}}, \quad 0<\alpha, \beta<\frac{\pi}{2}$ then $2 \beta$ is equal to

11Trigonometric Ratios And Identities

Simplified expression of
$1-\frac{\sin ^2 y}{1+\cos y}+\frac{1+\cos y}{\sin y}-\frac{\sin y}{1-\cos y}$ is :

12Trigonometric Ratios And Identities

If $\cos A=\frac{3}{4}$, then $\left(32 \sin \frac{A}{2} \sin \frac{5 A}{2}\right)=$

13Trigonometric Ratios And Identities

\(\text { If } \sin A=\frac{4}{5} \text { and } \cos B=\frac{-12}{13} \text { where } A \text { and } B \text { lie in first and third quadrant respectively. Then } \cos (A+B)=\)

14Trigonometric Ratios And Identities

\(4\left(1+\cos \frac{\pi}{8}\right)\left(1+\cos \frac{3 \pi}{8}\right)\left(1+\cos \frac{5 \pi}{8}\right)\left(1+\cos \frac{7 \pi}{8}\right) \text { is equal to }\)

15Trigonometric Ratios And Identities

If \(\cos \theta=\frac{1}{2}\left(x+\frac{1}{x}\right)\) then \(\frac{1}{2}\left(x^2+\frac{1}{x^2}\right)=\)

16Trigonometric Ratios And Identities

\(\text { If } \frac{\cos x}{\cos (x-2 y)}=\lambda \text { then } \tan (x-y) \tan y=\)

17Trigonometric Ratios And Identities

\(\sqrt{2+\sqrt{2+\sqrt{2+2 \cos 8 \theta}}} \text { where } \theta \in\left[-\frac{\pi}{8}, \frac{\pi}{8}\right] \text { is equal to }\)

18Trigonometric Ratios And Identities

\(\text { Value of } \cos 105^{\circ} \text { is }\)

19Trigonometric Ratios And Identities

\(\text { If } \frac{x}{\cos \theta}=\frac{y}{\cos \left(\theta+\frac{2 \pi}{3}\right)}=\frac{z}{\cos \left(\theta-\frac{2 \pi}{3}\right)} \text { then } x+y+z \text { is equal to }\)

20Trigonometric Ratios And Identities

\(\frac{\cos 9^{\circ}+\sin 9^{\circ}}{\cos 9^{\circ}-\sin 9^{\circ}}=\)

21Trigonometric Ratios And Identities

\(\left(\cos \frac{\pi}{12}-\sin \frac{\pi}{12}\right)\left(\tan \frac{\pi}{12}+\cot \frac{\pi}{12}\right)=\)

22Trigonometric Ratios And Identities

If \(\cos \alpha=k \cos \beta\) then \(\cot \left(\frac{\alpha+\beta}{2}\right)\) is equal to

23Trigonometric Ratios And Identities

\(\cos ^6 A-\sin ^6 A \text { is equal to }\)

24Trigonometric Ratios And Identities

\(\text { If } \operatorname{cosec}(90+A)+x \cos A \cot (90+A)=\sin (90+A) \text { then the value of } x \text { is }\)

25Trigonometric Ratios And Identities

The expression \(\frac{2 \tan A}{1-\cot A}+\frac{2 \cot A}{1-\tan A}\) can be written as

26Trigonometric Ratios And Identities

If \(\cos A=m \cos B\) and \(\cot \left(\frac{A+B}{2}\right)=\lambda \tan \left(\frac{B-A}{2}\right)\), then \(\lambda\) is equal to

27Trigonometric Ratios And Identities

What is \({{\cos \theta } \over {1 - \tan \theta }} + {{\sin \theta } \over {1 - \cot \theta }}\) equal to?

28Trigonometric Ratios And Identities

If \(\sin A+\sin B=a\) and \(\cos A+\cos B=b\), then \(\cos (A+B)\) equals?

29Trigonometric Ratios And Identities

The expression \({{\tan A} \over {1 - \cot A}} + {{\cot A} \over {1 - \tan A}}\) can be written as

30Trigonometric Ratios And Identities

If x and y are acute angles, such that \(\cos x + \cos y = {3 \over 2}\) and \(\sin x + \sin y = {3 \over 4}\), then \(\sin (x + y)\) equals

31Trigonometric Ratios And Identities

\({\sin ^2}17.5^\circ + \sin 72.5^\circ\) is equal to