If $2y\,\cos \theta = x\sin \,\theta {\rm{ and }}2x\sec \theta - y\,{\rm{cosec}}\,\theta = 3,$ then ${x^2} + 4{y^2} = $
The equation ${\sin ^2}\theta = \frac{{{x^2} + {y^2}}}{{2xy}},x,y, \ne 0$ is possible if
If $\theta $ and $\phi $ are angles in the $1^{st}$ quadrant such that $\tan \theta = 1/7$ and $\sin \phi = 1/\sqrt {10} $.Then
If $x + \frac{1}{x} = 2\cos \alpha $, then ${x^n} + \frac{1}{{{x^n}}} = $
Find the angle in radian through which a pendulum swings if its length is $75\, cm$ and the tip describes an arc of length.
$21\,cm$