List of top Mathematics Questions on Trigonometry asked in KEAM

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

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

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

The value of \( \tan \dfrac{\pi}{12}+\tan \dfrac{\pi}{6}+\left(\tan \dfrac{\pi}{12}\tan \dfrac{\pi}{6}\right) \) is equal to

If $\tan(x-y)=\frac{4}{5}$, $\tan(x+y)=\frac{6}{5}$ and $0<x,y<\frac{\pi}{4}$, then $\tan 2x$ is:

If $\tan^{-1}x = \tan^{-1}(3) - \frac{\pi}{4}$, then $x$ is equal to:

If $\sin^{-1}\left(\frac{x}{1+x}\right) = \frac{\pi}{2} - \cos^{-1}\left(\frac{1}{2}\right)$, then $x$ is equal to:

$\frac{(2 \sin \alpha)(1 + \sin \alpha)}{(1 + \sin \alpha + \cos \alpha)(1 + \sin \alpha - \cos \alpha)} =$

$\frac{\cos 75^{\circ} - \cos 15^{\circ}}{\cos 75^{\circ} + \cos 15^{\circ}} =$

$2^2 \sin(\frac{x}{2^2}) \cos(\frac{x}{2}) \cos(\frac{x}{2^2}) =$

If $\sin \theta = \frac{1}{5}$ and the angle $\theta$ is in the second quadrant, then $\sec \theta$ is equal to:

$\sin 15^{\circ} \sin 45^{\circ} \sin 75^{\circ} =$