Solve for $x$ , ${sin}^{2} 2 x = (sin 2 x)$

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Solution

Given
$s i n^{2} 2 x = s i n 2 x$
$\Rightarrow s i n 2 x (s i n 2 x - 1) = 0$
$\Rightarrow s i n 2 x = 0$ OR $s i n 2 x = 1$
For $n ϵ / z$
$\Rightarrow 2 x = n π$ OR $2 x = (2 n + 1) \frac{π}{2}$
$\Rightarrow x = \frac{n π}{2}$ $\Rightarrow x = (2 n + 1) \frac{π}{4}$

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