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

2 cos^{2} (x) = 3

9 tan (2 x) - 9 cot (x) = 0

sin (2 x) = 2 sin^{2} (x)

sin (x) sec (x) = sin (x)

cos (x) + 2 = 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