If $x\sin 45^\circ {\cos ^2}60^\circ = \frac{{{{\tan }^2}60^\circ {\rm{cosec}}30^\circ }}{{\sec 45^\circ {{\cot }^2}30^\circ }},$ then $x = $
$2$
$4$
$8$
$16$
Find the values of other five trigonometric functions if $\sec x=\frac{13}{5}, x$ lies in fourth quadrant.
If $\tan \theta + \sin \theta = m$ and $\tan \theta - \sin \theta = n,$ then
If $x = a{\cos ^3}\theta ,y = b{\sin ^3}\theta ,$ then
The equation ${(a + b)^2} = 4ab\,{\sin ^2}\theta $ is possible only when
Find the angle in radian through which a pendulum swings if its length is $75\, cm$ and the tip describes an arc of length.
$15\,cm$