Question

Find the number of solution of the equation ${\sin }^2\frac{x}{2}.\sin x+1=0$

Answer 1

${\sin }^2\frac{x}{2}.\sin x+1=0$
${\sin }^2\frac{x}{2}.\sin x=-1$
Only possible when $\sin x=-1$ and
$\sin \frac{x}{2}=\pm 1$ [both at same times]
But for any $x$ it is not possible
So, solution