List of top Mathematics Questions on Trigonometric Functions asked in KEAM

If $\tan \alpha = \frac{1}{2}$, then the value of $\tan^2(2\alpha) \sec^2(2\alpha)$ is equal to
The value of \[ \tan\!\left(\tan^{-1}(3)+\tan^{-1}(7)\right) \] is equal to:

\(\int \frac{1}{(1 - \cos x)}(1 + \sec x) dx = \) 
 

Let \(f(x)=2\sqrt{\,2\sin x+2\sqrt{2}\cos x\,},\; x\in\mathbb{R}\). Then the value of \(f\!\left(\frac{\pi}{12}\right)\) is equal to
If \(\text{cosec } t + \cot t = \frac{5}{2}\), then the value of \(\tan t\) is equal to
If \(\sin \theta = \frac{3}{5}\) and \(\cos \theta < 0\), then the value of \(\tan \theta\) is
$\tan(315^{\circ}) \cot(-405^{\circ}) = $ ________.
$\cos 75^{\circ} \cos 45^{\circ} \cos 15^{\circ} = $ ________.
The value of \( \sec^2(\tan^{-1} 3) + \csc^2(\cot^{-1} 2) \) is equal to:
The value of \( \sec^2(\tan^{-1} 3) + \csc^2(\cot^{-1} 2) \) is equal to:
The value of \( \sec^2(\tan^{-1} 3) + \csc^2(\cot^{-1} 2) \) is equal to: