`2sin(2x) + sqrt(3) = 0` Solve the multiple-angle equation.

Textbook Question

Chapter 5, 5.3 - Problem 40 - Precalculus (3rd Edition, Ron Larson).
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Borys Shumyatskiy | College Teacher | (Level 3) Associate Educator

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`2sin(2x)+sqrt(3)=0,`

`sin(2x) = -sqrt(3)/2.`

The general solution is

`2x = (-1)^k*arcsin(-sqrt(3)/2)+kpi,` `kinZZ.`

Because `arcsin(-sqrt(3)/2) = -pi/3,` the final answer is

`x=(-1)^(k+1)*(pi/6)+(kpi)/2, kinZZ`

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