What is the general solution for 4sin(2x)+2sqrt(3)=0 ?

The general solution for 4sin(2x)+2sqrt(3)=0 is x=(2pi)/3+pin,x=(5pi)/6+pin

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4sin(2x)+2sqrt(3)=0

4 sin (2 x) + 23 = 0

x = \frac{2 π}{3} + πn, x = \frac{5 π}{6} + πn

Solution steps

4 sin (2 x) + 23 = 0

Move

23

to the right side

4 sin (2 x) = - 23

Divide both sides by

4

sin (2 x) = - \frac{3}{2}

General solutions for

sin (2 x) = - \frac{3}{2}

2 x = \frac{4 π}{3} + 2 πn, 2 x = \frac{5 π}{3} + 2 πn

Solve

2 x = \frac{4 π}{3} + 2 πn : x = \frac{2 π}{3} + πn

Solve

2 x = \frac{5 π}{3} + 2 πn : x = \frac{5 π}{6} + πn

x = \frac{2 π}{3} + πn, x = \frac{5 π}{6} + πn

x, 3 = 18 cos (x)

x, 2 sin (\frac{π ( x - 2 )}{6}) = 1

(1 - sin (x)) (1 - sin (x)) = cos^{2} (x)

2 cos (x) = cos^{2} (x) - 1

2 sin (v) csc (v) - csc (v) = 4 sin (v) - 2

What is the general solution for 4sin(2x)+2sqrt(3)=0 ?
The general solution for 4sin(2x)+2sqrt(3)=0 is x=(2pi)/3+pin,x=(5pi)/6+pin