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

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Solution

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

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

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

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

Hence, no solution.

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