List of top Mathematical Ability Questions on Trigonometry asked in APICET

If $a \sin\theta + b \cos\theta = c$, then $(a \cos\theta - b \sin\theta)^2 = ?$

If $\pi/2 < x < \pi$ and $\tan x = -3/4$, then $\cos x = ?$

$(\cot A - \cos A)/(\cot A + \cos A) - (\csc A - 1)/(\csc A + 1) = ?$

The sides of a triangle are in the ratio 3:4:5. Then the measure (in degrees) of the largest angle of the triangle is:

If $\theta = 30^\circ$, then the value of \[ \frac{\sin^2\theta - \cos 2\theta}{\sin 2\theta + \cos^2\theta} \] is:

If $\sin\theta = \frac{3}{5}$ and $\theta<90^\circ$, then \[ \frac{\tan\theta - 2\cos\theta}{3\sin\theta + \sec\theta} = ? \]}