What is the general solution for 2sin(x/2)=1 ?

The general solution for 2sin(x/2)=1 is x= pi/3+4pin,x=(5pi)/3+4pin

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2sin(x/2)=1

2 sin (\frac{x}{2}) = 1

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

Solution steps

2 sin (\frac{x}{2}) = 1

Divide both sides by

2

sin (\frac{x}{2}) = \frac{1}{2}

General solutions for

sin (\frac{x}{2}) = \frac{1}{2}

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

Solve

\frac{x}{2} = \frac{π}{6} + 2 πn : x = \frac{π}{3} + 4 πn

Solve

\frac{x}{2} = \frac{5 π}{6} + 2 πn : x = \frac{5 π}{3} + 4 πn

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

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

cos (2 x + \frac{π}{3}) = sin (3 x)

y, x = arcsin (y)

2 sin^{2} (x) + 5 sin (x) = 3

∣ sin (x) ∣ = \frac{1}{2}

What is the general solution for 2sin(x/2)=1 ?
The general solution for 2sin(x/2)=1 is x= pi/3+4pin,x=(5pi)/3+4pin