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

The general solution for 2sin^2(x/2)-1=sin(x/2) is x=pi+4pin,x=(7pi)/3+4pin,x=(11pi)/3+4pin

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

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

x = π + 4 πn, x = \frac{7 π}{3} + 4 πn, x = \frac{11 π}{3} + 4 πn

Solution steps

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

Solve by substitution

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

sin (\frac{x}{2}) = 1 : x = π + 4 πn

sin (\frac{x}{2}) = - \frac{1}{2} : x = \frac{7 π}{3} + 4 πn, x = \frac{11 π}{3} + 4 πn

Combine all the solutions

x = π + 4 πn, x = \frac{7 π}{3} + 4 πn, x = \frac{11 π}{3} + 4 πn

4.7 2^{2} = 3. 3^{2} + 3. 3^{2} - 2 (3.3) (3.3) cos (x)

2 sin (x - 3 0^{\circ}) = cos (x - 6 0^{\circ})

1 = 2 cos (3 x)

sec (b) = \frac{1}{2}

2 cos (2 x) = sin (2 x)

What is the general solution for 2sin^2(x/2)-1=sin(x/2) ?
The general solution for 2sin^2(x/2)-1=sin(x/2) is x=pi+4pin,x=(7pi)/3+4pin,x=(11pi)/3+4pin