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

The general solution for 1-cos(x/2)=cos(x/2) is x=(2pi)/3+4pin,x=(10pi)/3+4pin

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

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

x = \frac{2 π}{3} + 4 πn, x = \frac{10 π}{3} + 4 πn

Solution steps

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

Solve by substitution

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

cos (\frac{x}{2}) = \frac{1}{2} : x = \frac{2 π}{3} + 4 πn, x = \frac{10 π}{3} + 4 πn

Combine all the solutions

x = \frac{2 π}{3} + 4 πn, x = \frac{10 π}{3} + 4 πn

2 cos^{2} (θ) + 2 cos (θ) - 1 = 0

- 2 sin (- 3 x) - 1 = 0

tan (x) + sin (x) tan (x) = 0, - π \leq x < π

4 sin^{2} (x) - sin (x) - 2 = 0

2 cos (x) sin (x) + 1 cos (x) = 0

What is the general solution for 1-cos(x/2)=cos(x/2) ?
The general solution for 1-cos(x/2)=cos(x/2) is x=(2pi)/3+4pin,x=(10pi)/3+4pin