WBJEE PYQs for Trigonometric Equations with Solutions: Practice WBJEE Previous Year Questions

Updated on - Dec 31, 2025

Trigonometric Equations is an important topic in the Mathematics section in WBJEE exam. Practising this topic will increase your score overall and make your conceptual grip on WBJEE exam stronger.

This article gives you a full set of WBJEE PYQs for Trigonometric Equations with explanations for effective preparation. Practice of WBJEE Mathematics PYQs including Trigonometric Equations questions regularly will improve accuracy, speed, and confidence in the WBJEE 2026 exam.

WBJEE PYQs for Trigonometric Equations with Solutions

1.
The equation $\sqrt{3}\, \sin \,x+\cos\,x = 4$ has
- only one solution
- two solutions
- infinitely many solutions
- no solution
View Solution
2.
The trigonometric equation $\sin^{-1}x = 2 \sin^{-1}2a$ has a real solution if
- $\left|a\right| > \frac{1}{\sqrt{2}}$
- $ \frac{1}{2\sqrt{2}} < \left|a\right| > \frac{1}{\sqrt{2}}$
- $ \left|a\right| > \frac{1}{2\sqrt{2}}$
- $ \left|a\right| \le \frac{1}{2\sqrt{2}}$
View Solution
3.
If $\sin ^{-1} x+\sin ^{-1} y+\sin ^{-1} z=\frac{3 \pi}{2}$, then the value of $x^{9}+y^{9}+z^{9}-\frac{1}{x^{9} y^{9} z^{9}}$ is equal to
- 0
- 1
- 2
- 3
View Solution
4.
If $ 0 \leq a, b \leq 3 $ and the equation $ x^2 + 4 + 3\cos(ax + b) = 2x $ has real solutions, then the value of $ (a + b) $ is:
- $ \frac{\pi}{4} $
- $ \frac{\pi}{2} $
- $ \pi $
- $ 2\pi $
View Solution
5.
The solution set of the equation $ \tan(\pi \tan x) = \cot(\pi \cot x) $, $ x \in \left(0, \frac{\pi}{2}\right) $, is:
- $ \{0\} $
- $ \left\{ \frac{\pi}{4} \right\} $
- $ \phi $
- $ \left\{ \frac{\pi}{6} \right\} $
View Solution
6.
The minimum value of $\cos\,\theta + \sin\,\theta+\frac{2}{\sin\,2\theta}$ for $\theta\,\in \left(0, \pi/2\right)$ is
- $2+\sqrt{2}$
- $2$
- $1+\sqrt{2}$
- $2\sqrt{2}$
View Solution

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WBJEE PYQs for Trigonometric Equations with Solutions: Practice WBJEE Previous Year Questions

WBJEE PYQs for Trigonometric Equations with Solutions

1.
The equation $\sqrt{3}\, \sin \,x+\cos\,x = 4$ has

2.
The trigonometric equation $\sin^{-1}x = 2 \sin^{-1}2a$ has a real solution if

3.
If $\sin ^{-1} x+\sin ^{-1} y+\sin ^{-1} z=\frac{3 \pi}{2}$, then the value of $x^{9}+y^{9}+z^{9}-\frac{1}{x^{9} y^{9} z^{9}}$ is equal to

4.
If \( 0 \leq a, b \leq 3 \) and the equation \( x^2 + 4 + 3\cos(ax + b) = 2x \) has real solutions, then the value of \( (a + b) \) is:

5.
The solution set of the equation \( \tan(\pi \tan x) = \cot(\pi \cot x) \), \( x \in \left(0, \frac{\pi}{2}\right) \), is:

6.
The minimum value of $\cos\,\theta + \sin\,\theta+\frac{2}{\sin\,2\theta}$ for $\theta\,\in \left(0, \pi/2\right)$ is

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WBJEE PYQs for Trigonometric Equations with Solutions

1.The equation $\sqrt{3}\, \sin \,x+\cos\,x = 4$ has

2.The trigonometric equation $\sin^{-1}x = 2 \sin^{-1}2a$ has a real solution if

3.If $\sin ^{-1} x+\sin ^{-1} y+\sin ^{-1} z=\frac{3 \pi}{2}$, then the value of $x^{9}+y^{9}+z^{9}-\frac{1}{x^{9} y^{9} z^{9}}$ is equal to

4.If \( 0 \leq a, b \leq 3 \) and the equation \( x^2 + 4 + 3\cos(ax + b) = 2x \) has real solutions, then the value of \( (a + b) \) is:

5.The solution set of the equation \( \tan(\pi \tan x) = \cot(\pi \cot x) \), \( x \in \left(0, \frac{\pi}{2}\right) \), is:

6.The minimum value of $\cos\,\theta + \sin\,\theta+\frac{2}{\sin\,2\theta}$ for $\theta\,\in \left(0, \pi/2\right)$ is

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1.
The equation $\sqrt{3}\, \sin \,x+\cos\,x = 4$ has

2.
The trigonometric equation $\sin^{-1}x = 2 \sin^{-1}2a$ has a real solution if

3.
If $\sin ^{-1} x+\sin ^{-1} y+\sin ^{-1} z=\frac{3 \pi}{2}$, then the value of $x^{9}+y^{9}+z^{9}-\frac{1}{x^{9} y^{9} z^{9}}$ is equal to

4.
If \( 0 \leq a, b \leq 3 \) and the equation \( x^2 + 4 + 3\cos(ax + b) = 2x \) has real solutions, then the value of \( (a + b) \) is:

5.
The solution set of the equation \( \tan(\pi \tan x) = \cot(\pi \cot x) \), \( x \in \left(0, \frac{\pi}{2}\right) \), is:

6.
The minimum value of $\cos\,\theta + \sin\,\theta+\frac{2}{\sin\,2\theta}$ for $\theta\,\in \left(0, \pi/2\right)$ is