$\frac{{\sin \theta }}{{1 - \cot \theta }} + \frac{{\cos \theta }}{{1 - \tan \theta }} = $
$0$
$1$
$\cos \theta - \sin \theta $
$\cos \theta + \sin \theta $
If $\sin \theta + {\rm{cosec}}\theta = 2,$ the value of ${\sin ^{10}}\theta + {\rm{cose}}{{\rm{c}}^{10}}\theta $ is
Find the angle in radian through which a pendulum swings if its length is $75\, cm$ and the tip describes an arc of length.
$21\,cm$
Find the value of $\cos \left(-1710^{\circ}\right)$.
The value of $2({\sin ^6}\theta + {\cos ^6}\theta ) - 3({\sin ^4}\theta + {\cos ^4}\theta ) + 1$ is
If $\cos (\alpha - \beta ) = 1$ and $\cos (\alpha + \beta ) = \frac{1}{e}$, $ - \pi < \alpha ,\beta < \pi $, then total number of ordered pair of $(\alpha ,\beta )$ is