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

The general solution for 2sin(x/2)+sqrt(3)=0 is x=(8pi)/3+4pin,x=(10pi)/3+4pin

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

2 sin (\frac{x}{2}) + 3 = 0

x = \frac{8 π}{3} + 4 πn, x = \frac{10 π}{3} + 4 πn

Solution steps

2 sin (\frac{x}{2}) + 3 = 0

Move

3

to the right side

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

Divide both sides by

2

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

General solutions for

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

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

Solve

\frac{x}{2} = \frac{4 π}{3} + 2 πn : x = \frac{8 π}{3} + 4 πn

Solve

\frac{x}{2} = \frac{5 π}{3} + 2 πn : x = \frac{10 π}{3} + 4 πn

x = \frac{8 π}{3} + 4 πn, x = \frac{10 π}{3} + 4 πn

2 cos^{2} (x) + 3 sin (x) = 0

tan (3 x) - 1 = 0

2 sin (2 x) - 1 = 0

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

csc (x) + 1 = 0

What is the general solution for 2sin(x/2)+sqrt(3)=0 ?
The general solution for 2sin(x/2)+sqrt(3)=0 is x=(8pi)/3+4pin,x=(10pi)/3+4pin