Prove: $sin x + {sin}^{2} x = 2$ find x

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Solution

$sin x + {sin}^{2} x = 2$
Let $y = sin x$
$i m p l i e s y + y^{2} = 2 y^{2} + y - 2 = 0 y = 1, - 2$
$sin x = 1 x = {sin}^{- 1} 1 = \frac{π}{2}$

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