If $\sin A = n\sin B,$ then $\frac{{n - 1}}{{n + 1}}\tan \,\frac{{A + B}}{2} = $
$\sin \frac{{A - B}}{2}$
$\tan \frac{{A - B}}{2}$
$\cot \frac{{A - B}}{2}$
None of these
$\cos \frac{\pi }{7}\cos \frac{{2\pi }}{7}\cos \frac{{3\pi }}{7} =$
The value of $sin\,10^o$ $sin\,30^o$ $sin\,50^o$ $sin\,70^o$ is
If $x\cos \theta = y\cos \,\left( {\theta + \frac{{2\pi }}{3}} \right) = z\cos \,\left( {\theta + \frac{{4\pi }}{3}} \right),$ then the value of $\frac{1}{x} + \frac{1}{y} + \frac{1}{z}$ is equal to
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
$\sqrt {\frac{{1 - \sin A}}{{1 + \sin A}}} = $