The expression $\frac{{\cos 6x + 6\cos 4x + 15\cos 2x + 10}}{{\cos 5x + 5\cos 3x + 10\cos x}}$ is equal to
$\cos 2x$
$2\cos x$
${\cos ^2}x$
$1 + \cos x$
If $x = \cos 10^\circ \cos 20^\circ \cos 40^\circ ,$ then the value of $x$ is
If $A + B + C = \frac{{3\pi }}{2},$ then $\cos 2A + \cos 2B + \cos 2C = $
$cot 5^o$ -$tan5^o$ -$2$ $tan10^o$ -$4$ $tan 20^o$ -$8$ $cot40^o$ 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
If $\sin A = n\sin B,$ then $\frac{{n - 1}}{{n + 1}}\tan \,\frac{{A + B}}{2} = $