What is the general solution for 3cos(x)=cos(x)-1 ?

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

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3cos(x)=cos(x)-1

3 cos (x) = cos (x) - 1

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

Solution steps

3 cos (x) = cos (x) - 1

Solve by substitution

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

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

Combine all the solutions

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

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

3 sin^{2} (x) = cos^{2} (x) - 4 cos (x)

cos (x) = 0.9224

- 9 sin^{2} (θ) + 3 cos (θ) - 2 = - 9

4 sin (x) = 4 cos (x)

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