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 \(x = \frac{1 + \cos 2\theta}{\tan \theta - \sec \theta}\) and \(y = \frac{\tan \theta + \sec \theta}{\sec^2 \theta}\), then \(\frac{y}{x}\) is equal to:

\(\cot^{-1}(1) + \cot^{-1}(2) + \cot^{-1}(3) =\)

If \(\tan\left(\alpha - \frac{\pi}{12}\right) = \frac{1}{\sqrt{3}}\), where \(0 < \alpha < \frac{\pi}{2}\), then the value of \(\alpha\) is equal to

If \(\cos\left(2\sin^{-1}\alpha\right) = \frac{47}{72}\), where \(0 < \alpha < 1\), then the value of \(\alpha\) is

\(\frac{3\tan 15^{\circ} - \tan^3 15^{\circ}}{1 - 3\tan^2 15^{\circ}}\)

\(x = \frac{1 + \cos 2\theta}{\tan \theta - \sec \theta}\) and \(y = \frac{\tan \theta + \sec \theta}{\sec^2 \theta}\), then \(\frac{y}{x} =\)

\(\sin 60^{\circ} - \sin 80^{\circ} + \sin 100^{\circ} - \sin 120^{\circ} =\)

If \(\cos^{-1} x - \sin^{-1} x = \frac{\pi}{6}\), then \(x\) is equal to

Let \( f(x) = |\sin 3x| - |\cos 3x| \), where \( \frac{\pi}{6} \le x \le \frac{\pi}{3} \). Then the value of \( f\left(\frac{\pi}{4}\right) \) is

If \( \theta = \cot^{-1}\sqrt{\frac{1-x}{1+x}} \), then \( \sec^2 \theta \) is equal to

\( \tan 15^\circ + \tan 75^\circ = \)

If \( x + z = 2y \) and \( y = \frac{\pi}{4} \), then \( \tan x \tan y \tan z = \)

If \( \sin x + \sin y = a \), \( \cos x + \cos y = b \) and \( x + y = \frac{2\pi}{3} \), then the value of \( \frac{a}{b} \) is equal to

If \( \sin \alpha = \frac{12}{13} \), where \( \frac{\pi}{2}<\alpha<\frac{3\pi}{2} \), then the value of \( \tan \alpha \) is equal to