$\sin {163^o}\cos {347^o} + \sin {73^o}\sin {167^o} = $
$0$
$1/2$
$1$
None of these
The value of $\cos 15^\circ - \sin 15^\circ $ is equal to
If $2\sec 2\alpha = \tan \beta + \cot \beta ,$ then one of the values of $\alpha + \beta $ is
${\sin ^4}\frac{\pi }{8} + {\sin ^4}\frac{{3\pi }}{8} + {\sin ^4}\frac{{5\pi }}{8} + {\sin ^4}\frac{{7\pi }}{8} = $
$A, B, C$ are the angles of a triangle, then ${\sin ^2}A + {\sin ^2}B + {\sin ^2}C - 2\cos A\,\cos B\,\cos C = $
The value of $\frac{{3 + \cot \,7\,{6^ \circ }\,\cot \,{{16}^ \circ }}}{{\cot \,{{76}^ \circ } + \cot \,{{16}^ \circ }}}$ is :