What is the general solution for sqrt((1-cos(x))/2)+cos(x)-1=0 ?

The general solution for sqrt((1-cos(x))/2)+cos(x)-1=0 is x=2pin,x= pi/3+2pin,x=(5pi)/3+2pin

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sqrt((1-cos(x))/2)+cos(x)-1=0

\frac{1 - cos ( x )}{2} + cos (x) - 1 = 0

x = 2 πn, x = \frac{π}{3} + 2 πn, x = \frac{5 π}{3} + 2 πn

Solution steps

\frac{1 - cos ( x )}{2} + cos (x) - 1 = 0

Solve by substitution

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

cos (x) = 1 : x = 2 πn

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

Combine all the solutions

x = 2 πn, x = \frac{π}{3} + 2 πn, x = \frac{5 π}{3} + 2 πn

arctan (x) = \frac{π}{6}

3 - cos (2 x) = 4 cos (2 x)

- 8 sin^{2} (x) + 22 sin (x) = 12

cos (θ) = \frac{1}{5}

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

What is the general solution for sqrt((1-cos(x))/2)+cos(x)-1=0 ?
The general solution for sqrt((1-cos(x))/2)+cos(x)-1=0 is x=2pin,x= pi/3+2pin,x=(5pi)/3+2pin