List of top Mathematics Questions on Trigonometry asked in KEAM

The value of \(2\tan^{-1}\left(\frac{1}{3}\right) + \cot^{-1}\left(\frac{3}{4}\right)\) is

The value of \(\cos^{-1}\left(-\frac{\sqrt{3}}{2}\right) + \sin^{-1}\left(\frac{1}{2}\right)\) is equal to

If \(\alpha\) and \(\beta\) are respectively the minimum and maximum values of \(\frac{\pi^2}{8} + 2\left(\sin^{-1}x - \frac{\pi}{4}\right)^2\), then \(\frac{\beta}{\alpha}\) is:

If \(\tan\left(\frac{\pi}{4} + \theta\right) = \frac{1}{2}\) then the value of \(\sin 2\theta\) is

If \(1 + \cos x = \alpha\), \(0 \leq x \leq \frac{\pi}{2}\), then \(\sin \frac{x}{2}\) is equal to

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

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

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

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

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

The value of $3\cot(-405^{\circ})\tan315^{\circ}-5\cot495^{\circ}\tan(-585^{\circ})$ is equal to

$\sin(\frac{3\pi}{4}+x)+\cos(\frac{3\pi}{4}+x)-\sin(\frac{3\pi}{4}-x)-\cos(\frac{3\pi}{4}-x)=$

$2^{11}\sin(\frac{x}{2^{10}})\cos(\frac{x}{2})\cos(\frac{x}{2^{2}})\cos(\frac{x}{2^{3}})\dots\cos(\frac{x}{2^{10}})$ is equal to

The value of $\sin 5^{\circ}\sin 10^{\circ}\sin 15^{\circ}\sin 20^{\circ}\dots\sin 240^{\circ}$ is equal to

The value of $\sin\left(2\sin^{-1}\frac{3}{5}\right)$ is equal to

The value of $\sin^{-1}\left(\sin \dfrac{5\pi}{9} \cos \dfrac{\pi}{9} + \sin \dfrac{\pi}{9} \cos \dfrac{5\pi}{9}\right)$ is equal to:

If $\tan \alpha = \dfrac{5}{6}$ and $\tan \beta = \dfrac{1}{11}$, where $0<\alpha,\beta<\dfrac{\pi}{2}$ then $\alpha + \beta =$:

The value of $\sin6^\circ \cos36^\circ \sin66^\circ + \cos12^\circ \sin42^\circ \sin18^\circ$ is equal to:

If $4\sin^2 x - 2(1+\sqrt{3})\sin x + \sqrt{3} = 0$ and $15^\circ<x<150^\circ$, then the values of $x$ are:

If $\sin \theta \cos \theta>0$, then $\theta$ lies

If \( \sin^{-1}x+\sin^{-1}y=\dfrac{2\pi}{3} \), then \( \cos^{-1}x+\cos^{-1}y \) is equal to

If \( \cos^{-1}x+\cos^{-1}y+\cos^{-1}z=3\pi \), then \( (x+y+z) \) is equal to

If \( \theta \in \left[\dfrac{\pi}{2}, \dfrac{3\pi}{2}\right] \), then \( \sin^{-1}(\sin\theta) \) is equal to

\(\frac{1-\cos 2x}{1+\cos 2x}-\sec^2 x=\)

The period of the function \(f(x)=2\sin 4x+3\cos 2x\) is