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

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

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sin(x/2)=1-sin(x/2)

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

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

Solution steps

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

Solve by substitution

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

sin (\frac{x}{2}) = \frac{1}{2} : x = \frac{π}{3} + 4 πn, x = \frac{5 π}{3} + 4 πn

Combine all the solutions

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

4 cos^{2} (θ) - 1 = 0

sinh (x) = 1

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

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

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

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