If $\cos \theta = \frac{1}{2}\left( {x + \frac{1}{x}} \right)$, then $\frac{1}{2}\left( {{x^2} + \frac{1}{{{x^2}}}} \right) = $
$\sin 2\theta $
$\cos \,2\theta $
$\tan \,2\theta $
$\sec \,2\theta $
If $\sin \theta + {\rm{cosec}}\theta = 2,$ the value of ${\sin ^{10}}\theta + {\rm{cose}}{{\rm{c}}^{10}}\theta $ is
Prove that: $\sin x+\sin 3 x+\sin 5 x+\sin 7 x=4 \cos x \cos 2 x \sin 4 x$
Find the value of the trigonometric function $\sin 765^{\circ}$
Find the angle in radian through which a pendulum swings if its length is $75\, cm$ and the tip describes an arc of length.
$21\,cm$
If $a\,{\cos ^3}\alpha + 3a\,\cos \alpha \,{\sin ^2}\alpha = m$ and $a\,{\sin ^3}\alpha + 3a\,{\cos ^2}\alpha \sin \alpha = n,$ then ${(m + n)^{2/3}} + {(m - n)^{2/3}}$ is equal to