$\frac{{\cos 12^\circ - \sin 12^\circ }}{{\cos 12^\circ + \sin 12^\circ }} + \frac{{\sin 147^\circ }}{{\cos 147^\circ }} = $
$1$
$-1$
$0$
None of these
If $A, B, C$ are acute positive angles such that $A + B + C = \pi $ and $\cot A\,\cot \,B\,\cot \,C = K,$ then
If $\cos \theta = \frac{1}{2}\left( {a + \frac{1}{a}} \right),$then the value of $\cos 3\theta $is
The value of $\frac{{3 + \cot {{76}^o}\cot {{16}^o}}}{{\cot {{76}^o} + \cot {{16}^o}}}$
If $\sin x + \cos x = \frac{1}{5},$ then $\tan 2x$ is
Prove that $\frac{\cos 4 x+\cos 3 x+\cos 2 x}{\sin 4 x+\sin 3 x+\sin 2 x}=\cot 3 x$