${\sin ^4}\frac{\pi }{8} + {\sin ^4}\frac{{3\pi }}{8} + {\sin ^4}\frac{{5\pi }}{8} + {\sin ^4}\frac{{7\pi }}{8} = $
$\frac{1}{2}$
$\frac{1}{4}$
$\frac{3}{2}$
$\frac{3}{4}$
If $\tan x + \tan \left( {\frac{\pi }{3} + x} \right) + \tan \left( {\frac{{2\pi }}{3} + x} \right) = 3,$ then
If $\alpha ,\,\,\beta ,\gamma ,\,\,\delta $ are the smallest positive angles in ascending order of magnitude which have their sines equal to the positive quantity $k$, then the value of $4\,\sin \frac{\alpha }{2} + 3\,\sin \frac{\beta }{2} + 2\,\sin \frac{\gamma }{2} + \sin \frac{\delta }{2}$ is equal to
The exact value of $cos^273^o + cos^247^o + (cos73^o . cos47^o )$ is
If $cos A = {3\over 4} , $ then $32\sin \left( {\frac{A}{2}} \right)\sin \left( {\frac{{5A}}{2}} \right) = $
${\sin ^4}\frac{\pi }{4} + {\sin ^4}\frac{{3\pi }}{8} + {\sin ^4}\frac{{5\pi }}{8} + {\sin ^4}\frac{{7\pi }}{8} = $