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

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

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cos(x)=1-cos(x)

cos (x) = 1 - cos (x)

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

Solution steps

cos (x) = 1 - cos (x)

Solve by substitution

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

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

Combine all the solutions

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

sin (\frac{θ}{2}) = - \frac{1}{2}

sec^{2} (x) = 3 tan (x) + 1

- 3 cos (2 θ) - sin (θ) - 6 = - 8

sin^{2} (x) + 1 = \frac{7}{2} cos^{2} (x)

cos (θ) sin (θ) - 2 cos (θ) = 0

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