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

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

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

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

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

Solution steps

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

3 = 4 - 2 sin (θ)

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

9 sin^{2} (x) tan (x) = 4 tan (x)

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

- 2 cos (θ) = 0

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