Question

The number of solution of equation $2\sin 2x+\sin x(1-2\cos 2x)-4=0$ in the interval $(0,\pi$) is -

Answer 1

$4\sin x\cos x+\sin x(1-2(2{\cos }^{2}x-1\left)\right)=4$

$4\cos x+1-4{\cos }^{2}x+2=\frac{4}{\sin x}$

$4-(2\cos x-1{)}^2=\frac{4}{\sin x}$

$\Rightarrow \text{L.H.S}\le 4$ and $\Rightarrow \text{R.H.S}\ge 4$ and equality holds when $\cos x=\frac{1}{2}$ and $\sin x=1$ which is not possible.

Hence, no solution.