Solve : $2 c o s^{2}$ $x$ + $3 s i n$ $x$ = 0

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Solution

$2 {cos}^{2} x + 3 sin x = 0$
$2 - 2 {sin}^{2} x + 3 sin x = 0$
$2 {sin}^{2} x - 3 sin x - 2 = 0$
$2 {sin}^{2} x - 4 sin x + sin x - 2 = 0$
$(2 sin x + 1) (sin x - 2) = 0)$
$⟹ sin x = - \frac{1}{2}$
$⟹ x = n π + (- 1)^{n} (\frac{- π}{6})$

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