List of top Mathematics Questions on Trigonometry asked in JEE Main

Let $K = \sin \frac{\pi}{18} \sin \frac{5\pi}{18} \sin \frac{7\pi}{18}$ then the value of $\sin \left( 10K \frac{\pi}{3} \right)$ is :

Let $x \in [-\pi, \pi]$ & $S = \{ x : \sin x (\sin x + \cos x) = a, a \in I \}$, then number of elements in set $S$ is equal to :

If \[ \frac{\tan(A-B)}{\tan A}+\frac{\sin^2 C}{\sin^2 A}=1, \quad A,B,C\in\left(0,\frac{\pi}{2}\right), \] then:

The least value of $(\cos^2 \theta - 6\sin \theta \cos \theta + 3\sin^2 \theta + 2)$ is

In \(\Delta ABC\) if \(\frac{\tan(A-B)}{\tan A} + \frac{\sin^2 C}{\sin^2 A} = 1\) where \(A, B, C \in (0, \frac{\pi}{2})\) then

Let \( \dfrac{\pi}{2} < \theta < \pi \) and \( \cot \theta = -\dfrac{1}{2\sqrt{2}} \). Then the value of \[ \sin\!\left(\frac{15\theta}{2}\right)(\cos 8\theta + \sin 8\theta) + \cos\!\left(\frac{15\theta}{2}\right)(\cos 8\theta - \sin 8\theta) \] is equal to

Let \( y = y(x) \) be the solution of the differential equation \( x^2 dy + (4x^2 y + 2\sin x)dx = 0 \), \( x>0 \), \( y\left(\frac{\pi}{2}\right) = 0 \). Then \( \pi^4 y\left(\frac{\pi}{3}\right) \) is equal to :

The value of \( \csc 10^\circ - \sqrt{3}\sec 10^\circ \) is:

Evaluate the limit: \[ \lim_{x \to 0} \frac{\sin(2x) - 2\sin x}{x^3} \]

The value of \(\text{cosec}10^\circ - \sqrt{3} \sec10^\circ\) is equal to:

The number of 4-letter words, with or without meaning, which can be formed using the letters PQRPRSTUVP, is :

Let \(\tan \left( \frac{\pi}{4} + \frac{1}{2} \cos^{-1} \frac{2}{3} \right) + \tan \left( \frac{\pi}{4} - \frac{1}{2} \sin^{-1} \frac{2}{3} \right) = k\). Then number of solution of the equation \(\sin^{-1}(kx - 1) = \sin x - \cos^{-1} x\) is/are :

If \[ k=\tan\!\left(\frac{\pi}{4}+\frac{1}{2}\cos^{-1}\!\left(\frac{2}{3}\right)\right) +\tan\!\left(\frac{1}{2}\sin^{-1}\!\left(\frac{2}{3}\right)\right), \] then the number of solutions of the equation \[ \sin^{-1}(kx-1)=\sin^{-1}x-\cos^{-1}x \] is:

Number of solutions in the interval \( [-2\pi, 2\pi] \) for the equation: \[ 2\sqrt{2} \cos^2 \theta + (2 - \sqrt{6}) \cos \theta - \sqrt{3} = 0 \]

The number of solutions of the equation $ 2x + 3\tan x = \pi $, $ x \in [-2\pi, 2\pi] - \left\{ \pm \frac{\pi}{2}, \pm \frac{3\pi}{2} \right\} $ is

The number of integral values of \(n\), for which the equation \[ 3\cos x + 5\sin x = 2n + 1 \] has a solution, is:

Let \( S = \{ x : \cos^{-1} x = \pi + \sin^{-1} x + \sin^{-1} (2x + 1) \ \). Then \[ \sum_{x \in S} (2x - 1)^2 \text{ is equal to:} \]

The number of solutions of the equation \( (4 - \sqrt{3}) \sin x - 2\sqrt{3} \cos^2 x = \frac{-4}{1 + \sqrt{3}} \), \( x \in \left[-2\pi, \frac{5\pi}{2}\right] \) is

The value of the following expression: $ \cot^{-1} \left( \frac{\sqrt{1 + \tan^2 2} + 1}{\tan 2} \right) - \cot^{-1} \left( \frac{\sqrt{1 + \tan^2 2} - 1}{\tan 2} \right) $

Let \( S = \{ x : \cos^{-1} x = \pi + \sin^{-1} x + \sin^{-1} (2x + 1) \ \). Then \[ \sum_{x \in S} (2x - 1)^2 \text{ is equal to:} \]

If \[ \sum_{r=1}^{13} \frac{1}{\sin \frac{\pi}{4} + (r-1) \frac{\pi}{6}} \sin \frac{\pi}{4} + \frac{\pi}{6} = a \sqrt{3} + b, \quad a, b \in \mathbb{Z}, { then } a^2 + b^2 { is equal to:} \]

If \[ \sum_{r=1}^{13} \frac{1}{\sin \frac{\pi}{4} + (r-1) \frac{\pi}{6}} \sin \frac{\pi}{4} + \frac{\pi}{6} = a \sqrt{3} + b, \quad a, b \in \mathbb{Z}, { then } a^2 + b^2 { is equal to:} \]

If $\sin x = -\frac{3}{5}$, where $\pi<x<\frac{3\pi}{2}$, then $80(\tan^2 x - \cos x)$ is equal to: