The value of $\cos (270^\circ + \theta )\,\cos (90^\circ - \theta ) - \sin (270^\circ - \theta )\,\cos \theta $ is

If $\sin \theta + \sin 2\theta + \sin 3\theta = \sin \alpha$ and $\cos \theta + \cos 2\theta + \cos 3\theta = \cos \alpha$,then $\theta$ is equal to

$(\sec A + \tan A - 1)(\sec A - \tan A + 1) - 2\tan A = $

Find the value of $\tan 4^{\circ} \tan 43^{\circ} \tan 47^{\circ} \tan 86^{\circ}$.

The equation $\sec^2 \theta = \frac{4xy}{(x + y)^2}$ is only possible when

Let $A = \{ \theta : 2\cos^2 \theta + \sin \theta \le 2 \}$ and $B = \{ \theta : \frac{\pi}{2} \le \theta \le \frac{3\pi}{2} \}$,then $A \cap B$ is