List of top Mathematics Questions on Trigonometry

If $\sin x \cos x = \frac{1}{4}$, then the general solution is:

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

If $\sin x \cos x = \frac{1}{4}$, then the general solution is:

In a $\triangle ABC$, $a = 1$, $b = \sqrt{3}$ and $\angle C = \dfrac{\pi}{6}$. Then the measure of the third side $c =$}

In a triangle $\triangle ABC$, if $a$, $b$, and $c$ are in arithmetic progression, then $\cos A + 2\cos B + \cos C =$

If the area of triangle $ABC$ is $b^2 - (c-a)^2$, then $\tan B =$

If \[ \sin^{-1}\frac{5}{x}+\sin^{-1}\frac{12}{x}=\frac{\pi}{2}, \] then \(x=\)

If \(2\sin^{-1}x=\sin^{-1}k\), then \(k=\)

If \(\tan A=\frac{1}{2}\) and \(\tan B=\frac{1}{3}\), then \(A+B=\)

\[ \cos 6^\circ \sin 24^\circ \cos 72^\circ= \]

\[ \tan^{-1}1+\tan^{-1}2+\tan^{-1}3= \]

\[ \frac{\tan x-1+\sec x}{\tan x-\sec x+1} = \]

If \( \tan\theta+\sec\theta=\sqrt{3} \), then the principal value of \( \theta \) in \( [0,2\pi] \) is

If \( \cos\theta=\frac{1}{2}\left(a+\frac{1}{a}\right) \), then \(4\cos^3\theta-3\cos\theta=\)

\[ \tan 9^\circ-\tan 27^\circ-\tan 63^\circ+\tan 81^\circ= \]

The number of solutions of the equation \( \sin 2x-\cos 2x=2-\sin 2x \) lying in the interval \( [0,\pi] \) is

Domain of $\cos^{-1}[x]$ is, where $[.]$ denotes greatest integer function:

Given $0 \le x \le \dfrac{1}{2}$ then the value of $\tan \left[ \sin^{-1} \left( \dfrac{x}{\sqrt{2}} + \dfrac{\sqrt{1-x^2}}{\sqrt{2}} \right) - \sin^{-1} x \right]$ is:

The angles of a triangle are in A.P and the greatest angle is double the least angle, then sine of the third angle is

If \( \tan^{-1}x + \tan^{-1}y = \frac{\pi}{4} \), then what is the value of \(x + y + xy\)?

Let $f(x)=(8\sin x+15\cos x+3)^{2}-15$, $x\in\mathbb{R}.$ Then the maximum value of $f$ is

The value of $\frac{\sqrt{3}(\sin 40^{\circ}+\sin 20^{\circ})}{\cos 40^{\circ}+\cos 20^{\circ}}$ is

The value of $4 \cos 36^{\circ}\cos 72^{\circ}$ is equal to

The value of $\frac{\tan 75^{\circ}+\tan 15^{\circ}}{\tan 75^{\circ}-\tan 15^{\circ}}$ is equal to

If $\sec^{2}\theta+\tan^{2}\theta=7, 0<\theta<\frac{\pi}{2}$, then $\tan 2\theta$ is equal to