$\tan 75^\circ - \cot 75^\circ = $
$2\sqrt 3 $
$2 + \sqrt 3 $
$2 - \sqrt 3 $
None of these
Let $0 < x < \frac{\pi }{4}.$ Then $\sec 2x - \tan 2x = $
Prove that $\frac{\cos 9 x-\cos 5 x}{\sin 17 x-\sin 3 x}=-\frac{\sin 2 x}{\cos 10 x}$
$1 + \cos 2x + \cos 4x + \cos 6x = $
If $\sin \theta + \cos \theta = x,$ then ${\sin ^6}\theta + {\cos ^6}\theta = \frac{1}{4}[4 - 3{({x^2} - 1)^2}]$ for
$\tan 5x\tan 3x\tan 2x = $