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

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

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

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

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

Solution steps

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

Solve by substitution

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

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

Combine all the solutions

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

sec (θ) = 2

2 cos^{2} (θ) - 3 cos (θ) + 1 = 0

cos (2 θ) = 1

sec^{2} (x) = 1

tan^{2} (θ) = 3

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