Trigonometric Ratios & Identities PYQs - Last 5 Years
TS EAMCET / Mathematics / Trigonometry / 75 recent questions
MathematicsTrigonometry2021-2025
Practice 75 TS EAMCET 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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2022-2025
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Last 5 Years Trigonometric Ratios & Identities Questions
Showing 50 of 75 filtered questions.
1Trigonometric Ratios And Identities
If $\cos \theta+\sin \theta=\sqrt{2} \cos \theta$ and $0<\theta<\frac{\pi}{2}$, then $\sec 2 \theta+\tan 2 \theta=$
MCQ+1 / -02025
2Trigonometric Ratios And Identities
If $x=\log _e 3$, then $\tanh 2 x+\operatorname{sech} 2 x=$
MCQ+1 / -02025
3Trigonometric Ratios And Identities
If $\cos \alpha=\frac{l \cos \beta+m}{l+m \cos \beta}$, then $\left(\frac{\tan \frac{\alpha}{2}}{\tan \frac{\beta}{2}}\right)^2=$
MCQ+1 / -02025
4Trigonometric Ratios And Identities
If $P=\sin \frac{2 \pi}{7}+\sin \frac{4 \pi}{7}+\sin \frac{8 \pi}{7}$ and $Q=\cos \frac{2 \pi}{7}+\frac{4 \pi}{7}+\cos \frac{8 \pi}{7}$, then the point $(P, Q)$ lies on the circle of radius
MCQ+1 / -02025
5Trigonometric Ratios And Identities
If $\tan \left(\frac{\pi}{4}+\frac{\alpha}{2}\right)=\tan ^3\left(\frac{\pi}{4}+\frac{\beta}{2}\right)$, then $\frac{3+\sin ^2 \beta}{1+3 \sin ^2 \beta}=$
MCQ+1 / -02025
6Trigonometric Ratios And Identities
$16 \sin 12^{\circ} \cos 18^{\circ} \sin 48^{\circ}=$
MCQ+1 / -02025
7Trigonometric Ratios And Identities
\(\frac{\cos 15^{\circ} \cos ^2 22 \frac{1^{\circ}}{2}-\sin 75^{\circ} \sin ^2 \cdot 52 \frac{1^{\circ}}{2}}{\cos ^2 15^{\circ}-\cos ^2 75^{\circ}}\)
MCQ+1 / -02025
8Trigonometric Ratios And Identities
If $3 \sin \theta+4 \cos \theta=3$ and $\theta \neq(2 n+1) \frac{\pi}{2}$, then $\sin 2 \theta=$
MCQ+1 / -02025
9Trigonometric Ratios And Identities
\(4 \cos \frac{7 \theta}{2} \cos \frac{3 \theta}{2} \sin 5 \theta=\)
MCQ+1 / -02025
10Trigonometric Ratios And Identities
If $\sin A=-\frac{24}{25}, \cos B=\frac{15}{17}, A$ does not belong to 4th quadrant and $B$ does not belong to 1st quadrant, then $(A+B)$ lies in the quadrant
MCQ+1 / -02025
11Trigonometric Ratios And Identities
$\cot h^2 x-\tanh ^2 x=$
MCQ+1 / -02025
12Trigonometric Ratios And Identities
If $1^{\circ}=0.0175$ radians, then the approximate value of $\sec 58^{\circ}$ is
MCQ+1 / -02025
13Trigonometric Ratios And Identities
If $A+B+C=4 S$, then $\sin (2 S-A)$
\(+\sin (2 S-B)+\sin (2 S-C)-\sin 2 S=\)
\(+\sin (2 S-B)+\sin (2 S-C)-\sin 2 S=\)
MCQ+1 / -02025
14Trigonometric Ratios And Identities
The period of the function $f(x)=\frac{2 \sin \left(\frac{\pi x}{3}\right) \cos \left(\frac{2 \pi x}{5}\right)}{3 \tan \left(\frac{7 \pi x}{2}\right)-5 \sec \left(\frac{5 \pi x}{3}\right)}$ is
MCQ+1 / -02025
15Trigonometric Ratios And Identities
If $\sin A=-\frac{60}{61}, \cot B=-\frac{40}{9}$ and neither $A$ and $B$ is in 4th quadrant, then $6 \cot A+4 \sec B=$
MCQ+1 / -02025
16Trigonometric Ratios And Identities
If $5 \sin \theta+3 \cos \left(\theta+\frac{\pi}{3}\right)+3$ lies between $\alpha$ and $\beta$ (including $\alpha, \beta$ also), then $(\alpha-\beta)(\alpha+\beta-6)=$
MCQ+1 / -02025
17Trigonometric Ratios And Identities
\(\frac{\sin 1^{\circ}+\sin 2^{\circ}+\ldots \sin 89^{\circ}}{2\left(\cos 1^{\circ}+\cos 2^{\circ}+\ldots+\cos 44^{\circ}\right)+1}=\)
MCQ+1 / -02025
18Trigonometric Ratios And Identities
If $3 \sin (\alpha-\beta)=5 \cos (\alpha+\beta)$ and $\alpha+\beta \neq \frac{\pi}{2}$, then $\frac{\tan \left(\frac{\pi}{4}-\alpha\right)}{\tan \left(\frac{\pi}{4}-\beta\right)}=$
MCQ+1 / -02025
19Trigonometric Ratios And Identities
If $\tan A<0$ and $\tan 2 A=-\frac{4}{3}$, then $\cos 6 A=$
MCQ+1 / -02024
20Trigonometric Ratios And Identities
If $m \cos (\alpha+\beta)-n \cos (\alpha-\beta)$ $=m \cos (\alpha-\beta)+n \cos (\alpha+\beta)$, then $\tan \alpha \tan \beta=$
MCQ+1 / -02024
21Trigonometric Ratios And Identities
The maximum value of the function $f(x)=3 \sin ^{12} x+4 \cos ^{16} x$ is
MCQ+1 / -02024
22Trigonometric Ratios And Identities
If $\cos x+\cos y=\frac{2}{3}$ and $\sin x-\sin y=\frac{3}{4}$, then $\sin (x-y)+\cos (x-y)=$
MCQ+1 / -02024
23Trigonometric Ratios And Identities
If $\theta$ is an acute angle and $2 \sin ^{2} \theta=\cos ^{4} \frac{\pi}{8}+\sin ^{4} \frac{3 \pi}{8}+\cos ^{4} \frac{5 \pi}{8}+\sin ^{4} \frac{7 \pi}{8}$, then $\theta=$
MCQ+1 / -02024
24Trigonometric Ratios And Identities
If $0 < B < A < \frac{\pi}{4}, \cos ^{2} B-\sin ^{2} A=\frac{\sqrt{3}+1}{4 \sqrt{2}}$ and $2 \cos A \cos B=\frac{1+\sqrt{2}+\sqrt{3}}{2 \sqrt{2}}$, then $\cos ^{2} \frac{4 B}{3}-\sin ^{2} \frac{4 A}{5}=$
MCQ+1 / -02024
25Trigonometric Ratios And Identities
If $2 \tan ^{2} \theta-4 \sec \theta+3=0$, then $2 \sec \theta=$
MCQ+1 / -02024
26Trigonometric Ratios And Identities
If $(\sin \theta-\operatorname{cosec} \theta)^{2}+(\cos \theta+\sec \theta)^{2}=5$ and $\theta$ lies in the third quadrant, then $(\sin \theta+\cos \theta)^{3}=$
MCQ+1 / -02024
27Trigonometric Ratios And Identities
If $\cos ^2 84^{\circ}+\sin ^2 126^{\circ}-\sin 84^{\circ} \cos 126^{\circ}=K$ and $\cot A+\tan A=2 K$, then the possible values of $\tan A$ are
MCQ+1 / -02024
28Trigonometric Ratios And Identities
The approximate value of $\sec 59^{\circ}$ obtained by taking $1^{\circ}$ $=0.0174$ and $\sqrt{3}=1.732$ is
MCQ+1 / -02024
29Trigonometric Ratios And Identities
$\tan A=\frac{-60}{11}$ and $A$ does not lie in the 4th quadrant. $\sec B=\frac{41}{9}$ and $B$ does not lie in the 1st quadrant. If $\operatorname{cosec} A+\cot B=K$, then $24 K=$
MCQ+1 / -02024
30Trigonometric Ratios And Identities
$\sin 20^{\circ}\left(4+\sec 20^{\circ}\right)=$
MCQ+1 / -02024
31Trigonometric Ratios And Identities
If $0 < \theta < \frac{\pi}{4}$ and $8 \cos \theta+15 \sin \theta=15$, then $15 \cos \theta-8 \sin \theta=$
MCQ+1 / -02024
32Trigonometric Ratios And Identities
If $\sin h x=\frac{12}{5}$, then $\sin h 3 x+\cos h 3 x=$
MCQ+1 / -02024
33Trigonometric Ratios And Identities
The quadratic equation whose roots are $\sin ^2 18^{\circ}$ and $\cos ^2 36^{\circ}$ is
MCQ+1 / -02023
34Trigonometric Ratios And Identities
If $\cos \theta=\frac{-3}{5}$ and $\pi<\theta<\frac{3 \pi}{2}$, then $\tan \frac{\theta}{2}+\sin \frac{\theta}{2}+2 \cos \frac{\theta}{2}=$
MCQ+1 / -02023
35Trigonometric Ratios And Identities
If $\sin x \cdot \cosh y=\cos \theta$ and $\cos x \cdot \sinh y=\sin \theta$, then $\sin ^2 x+\cosh ^2 y=$
MCQ+1 / -02023
36Trigonometric Ratios And Identities
If $\cos A+\cos B+\cos C=0=\sin A+\sin B+\sin C$, then $\cos (A-B)+\cos (B-C)+\cos (C-A)=$
MCQ+1 / -02023
37Trigonometric Ratios And Identities
If $\tan \beta=\frac{n \sin \alpha \cos \alpha}{1-n \cos ^2 \alpha}$, then $\tan (\alpha+\beta) \cdot \cot \alpha=$
MCQ+1 / -02023
38Trigonometric Ratios And Identities
If $\frac{\sin ^4 x}{2}+\frac{\cos ^4 x}{3}=\frac{1}{5}$, then $27 \sec ^6 \alpha+8 \operatorname{cosec}^6 \alpha=$
MCQ+1 / -02023
39Trigonometric Ratios And Identities
If $\cot \theta=-\frac{2}{3}$ and $\theta$ does not lie in the 4 th quadrant, then $\frac{(5 \sin \theta+\cos \theta)^2}{\tan \theta+\cot \theta}=$
MCQ+1 / -02023
40Trigonometric Ratios And Identities
If $540^{\circ}<\theta<630^{\circ}$ and $\tan \theta=5 / 12$, then
\(\frac{\cos \frac{\theta}{2}-5 \sin \frac{\theta}{2}}{\sqrt{-(12 \sec \theta+5 \operatorname{cosec} \theta)}}=\)
\(\frac{\cos \frac{\theta}{2}-5 \sin \frac{\theta}{2}}{\sqrt{-(12 \sec \theta+5 \operatorname{cosec} \theta)}}=\)
MCQ+1 / -02023
41Trigonometric Ratios And Identities
If $\cosh x=\frac{4}{3}$, then $3 \cosh x+3^2 \cosh 2 x+3^3 \cosh 3 x=$
MCQ+1 / -02023
42Trigonometric Ratios And Identities
If $A+B+C+D=2 \pi$, then $\cos A-\cos B+\cos C-\cos D=$
MCQ+1 / -02023
43Trigonometric Ratios And Identities
If $\tan \alpha=\frac{-12}{5}, \cot \beta=\frac{7}{24}, \alpha$ does not belong to second quadrant and $\beta$ does not belong to first quadrant, then $\sqrt{13} \sin \frac{\alpha}{2}+\cos \frac{\beta}{2}+\tan \frac{\alpha}{2} \cot \frac{\b...
MCQ+1 / -02023
44Trigonometric Ratios And Identities
\(\sin 6^{\circ}+\sin 54^{\circ}+\sin 126^{\circ}+\cos 156^{\circ}=\)
MCQ+1 / -02023
45Trigonometric Ratios And Identities
$\cos \frac{\pi}{7} \cos \frac{2 \pi}{7} \cos \frac{3 \pi}{7} \cos \frac{\pi}{14} \cos \frac{3 \pi}{14} \cos \frac{5 \pi}{14}=$
MCQ+1 / -02023
46Trigonometric Ratios And Identities
\(\frac{\left(1+\tan 32^{\circ}\right)}{\left(1-\tan 48^{\circ}\right)}=\)
MCQ+1 / -02023
47Trigonometric Ratios And Identities
For $0 \leq x \leq \pi$, if $81^{\sin ^2 x}+81^{\cos ^2 x}=30$, then $x=$
MCQ+1 / -02023
48Trigonometric Ratios And Identities
\(\sin \alpha+\cos \alpha=m \Rightarrow \sin ^6 \alpha+\cos ^6 \alpha=\)
MCQ+1 / -02023
49Trigonometric Ratios And Identities
If $f(\theta)=\cos ^3 \theta+\cos ^3\left(\frac{2 \pi}{3}+\theta\right)+\cos ^3\left(\theta-\frac{2 \pi}{3}\right)$, then $f\left(\frac{\pi}{5}\right)=$
MCQ+1 / -02023
50Trigonometric Ratios And Identities
If $\cos \frac{\pi}{7} \cos \frac{2 \pi}{7} \cos \frac{4 \pi}{7}=\frac{\sin \frac{8 \pi}{7}}{8 \sin \frac{\pi}{7}}$, then $\sin \frac{\pi}{14} \sin \frac{3 \pi}{14} \sin \frac{5 \pi}{14} \sin \frac{7 \pi}{14} \sin \frac{9 \pi}{14} \sin \fra...
MCQ+1 / -02023