List of top Mathematics Questions on Trigonometry asked in KEAM

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:

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

$\sec^{2}x + \csc^{2}x - \sec^{2}x \csc^{2}x =$

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

If \( 5\sin^{-1}\alpha + 3\cos^{-1}\alpha = \pi \), then \( \alpha \) is equal to

If \( f(x) = \tan^{-1}\left(\frac{2x}{1 - x^2}\right) \), then \( f\left(\frac{1}{\sqrt{3}}\right) \) 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

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

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

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 \(\frac{y}{x} =\)

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