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

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

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

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

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

Solution steps

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

Divide both sides by

23

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

General solutions for

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

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

Solve

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

Solve

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

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

2 cos (θ) = - 1

sin (θ) = \frac{2}{5}

cos (2 x) - cos (x) = 0, 0 \leq x \leq 2 π

cos (θ) = 2

sin (2 x) - tan (x) = 0

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