Trigonometric Equations PYQs - Last 5 Years

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All Trigonometric Equations PYQs Last 10 Years Create chapter test

Practice 32 AP EAPCET Mathematics questions from Trigonometric Equations. Use the year-wise and type-wise breakdown to prioritize recent PYQs, then continue into the question list below.

32

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Mathematics / Trigonometry

2021-2025

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32

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2021-2025

32

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2016-2025

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Last 5 Years Trigonometric Equations Questions

Showing 32 of 32 filtered questions.

1Trigonometric Equations

Statement I In the interval $[0,2 \pi]$, the number of common solutions of the equations $2 \sin ^2 \theta-\cos 2 \theta=0$ and $2 \cos ^2 \theta-3 \sin \theta=0$ is two.
Statement II The number of solutions of $2 \cos ^2 \theta-3 \sin \the...

2Trigonometric Equations

If $0 \leq x \leq 3$ and $0 \leq y \leq 3$, then the number of solutions $(x, y)$ of the equation $\left(\sqrt{\sin ^2 x-\sin x+\frac{1}{2}}\right) 2^{\sec ^2 y}=1$ is

3Trigonometric Equations

If $\tan \left(\frac{\pi}{4}+\alpha\right)=\tan ^3\left(\frac{\pi}{4}+\beta\right)$, then $\tan (\alpha+\beta) \cot (\alpha-\beta)=$

4Trigonometric Equations

The number of solutions of the equation $4 \cos 2 \theta \cos 3 \theta=\sec \theta$ in the interval $[0,2 \pi]$ is

5Trigonometric Equations

The sum of the solutions of $\cos x \sqrt{16 \sin ^2 x}=1$ in $(0,2 \pi)$ is

6Trigonometric Equations

\(\tan \frac{2 \pi}{7} \cdot \tan \frac{4 \pi}{7}+\tan \frac{4 \pi}{7} \cdot \tan \frac{\pi}{7}+\tan \frac{\pi}{7} \cdot \tan \frac{2 \pi}{7}=\)

7Trigonometric Equations

The number of solutions of the equation $\sec x \cdot \cos 5 x+1=0$ in the interval $[0,2 \pi]$ is

8Trigonometric Equations

If $\sqrt{3} \cos \theta+\sin \theta>0$, then

9Trigonometric Equations

The general solution satisfying both the equations $\sin x=-\frac{3}{5}$ and $\cos x=-\frac{4}{5}$ is

10Trigonometric Equations

The number of solutions of $\sin 2 x+\cos 4 x=2$ in the interval $[-\pi, \pi]$ is

11Trigonometric Equations

If $x \neq(2 n+1) \frac{\pi}{4}$, then the general solutions of $\cos x+\cos 3 x=\sin x+\sin 3 x$ is

12Trigonometric Equations

If $2 \sin x-\cos 2 x=1$, then $\left(3-2 \sin ^2 x\right)=$

13Trigonometric Equations

Number of solutions of the equation $\cos \theta+\cos 2 \theta-\sqrt{3}(\sin \theta+\sin 2 \theta)+1=0$ lying in the interval $(0,2 \pi)$ is

14Trigonometric Equations

The number of solutions of the equation $2 \sin ^2 \theta-3 \cos ^2 \theta=\sin \theta \cos \theta$ lying in the intervals $(-\pi, \pi)$ is

15Trigonometric Equations

The general solution of $\cot \frac{x}{2}-\cot x=\operatorname{cosec} \frac{x}{2}$ is

16Trigonometric Equations

The general solution of the equation $\tan x+\tan 2 x-\tan 3 x=0$ is

17Trigonometric Equations

The values of $x$ in $(-\pi, \pi)$, which satisfy the equation $8^{1+\cos ^2 x+\cos ^4 x+\ldots \ldots}=4^3$ are

18Trigonometric Equations

If the general solution .set of $\sin x+3 \sin 3 x+\sin 5 x=1$ is $S$, then $\{\sin \alpha / \alpha \in S\}=$

19Trigonometric Equations

For $a \in R-\{0\}$, if $a \cos x+a \sin x+a=2 k+1$ has a solution, then $k$ lies in the interval

20Trigonometric Equations

Number of solutions of the trigonometric equation $2 \tan 2 \theta-\cot 2 \theta+1=0$ lying in the interval $[0, \pi]$ is

21Trigonometric Equations

The number of ordered pairs $(x, y)$ satisfying the equations $\sin x+\sin y=\sin (x+y)$ and $|x|+|y|=1$ is

22Trigonometric Equations

If $5 \sin h x-\cos h x=5$, then one of the values of $\tan h x$ is

23Trigonometric Equations

The general solution of the equation $\sin ^2 \theta+3 \cos ^2 \theta=$ $5 \sin \theta$ is

24Trigonometric Equations

The general solution of $2 \cos ^2 x-2 \tan x+1=0$ is

25Trigonometric Equations

The smallest positive value (in degrees) of $\theta$ for which $\tan \left(\theta+100^{\circ}\right)=\tan \left(\theta+50^{\circ}\right) \tan (\theta) \tan \left(\theta-50^{\circ}\right)$ is valid, is

26Trigonometric Equations

The general solution of
$$ \begin{aligned} & 4 \cos 2 x-4 \sqrt{3} \sin 2 x+\cos 3 x-\sqrt{3} \sin 3 x \\ & \qquad+\cos x-\sqrt{3} \sin x=0 \end{aligned} $$

27Trigonometric Equations

$1+\sin x+\sin ^2 x+\sin ^3 x+\ldots \ldots+\infty=4+2 \sqrt{3}$ and $0

28Trigonometric Equations

If \(2 \cosh 2 x+10 \sinh 2 x=5\), then \(x=\)

29Trigonometric Equations

\(\text { If } \sin \theta+\operatorname{cosec} \theta=4, \text { then } \sin ^2 \theta+\operatorname{cosec}^2 \theta=\)

30Trigonometric Equations

If \(\sin \left(\frac{\pi}{4} \cos \theta\right)=\cos \left(\frac{\pi}{4} \tan \theta\right)\), then \(\theta\) is equal to

31Trigonometric Equations

The value of \(x\) satisfying the equation \(3 \operatorname{cosec} x=4 \sin x\) are

32Trigonometric Equations

If \(\theta \in[0,2 \pi]\) and \(\cos 2 \theta=\cos \theta+\sin \theta\), then the sum of all values of \(\theta\) satisfying the equation is