What are the principal solutions of the equation
$2 s i n^{2} x + (2 - \sqrt{3}) s i n x - \sqrt{3} = 0 ?$

$x = \frac{π}{3}$

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$x = - \frac{π}{3}$

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$x = \frac{π}{2}$

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$x = - \frac{π}{2}$

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Solution

The correct options are
A
$x = \frac{π}{3}$

D
$x = - \frac{π}{2}$

$2 s i n^{2} x + (2 - \sqrt{3}) s i n x - \sqrt{3} = 0 2 s i n^{2} x + 2 s i n x - \sqrt{3} s i n x - \sqrt{3} = 0 2 s i n x (s i n x + 1) - \sqrt{3} (s i n x + 1) = 0 (2 s i n x - \sqrt{3}) (s i n x + 1) = 0 s i n x = \frac{\sqrt{3}}{2} o r s i n x = - 1 x = \frac{π}{3} o r x = - \frac{π}{2}$

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