If $\tan x=\frac{3}{4}, \pi < x < \frac{3 \pi}{2},$ find the value of $\sin \frac{x}{2}, \cos \frac{x}{2}$ and $\tan \frac{x}{2}$
Prove that: $\sin x+\sin 3 x+\sin 5 x+\sin 7 x=4 \cos x \cos 2 x \sin 4 x$
Find the value of:
$\tan 15^{\circ}$
Prove that :
$\cot ^{2} \frac{\pi}{6}+\cos ec \,\frac{5 \pi}{6}+3 \tan ^{2}\, \frac{\pi}{6}=6$
If $\cos \theta - \sin \theta = \sqrt 2 \sin \theta ,$ then $\cos \theta + \sin \theta $ is equal to