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

Expert Answers
Borys Shumyatskiy eNotes educator| Certified Educator

`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`