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

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

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cos^3(x)=cos(x)

cos^{3} (x) = cos (x)

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

Solution steps

cos^{3} (x) = cos (x)

Solve by substitution

cos (x) = 0, cos (x) = - 1, cos (x) = 1

cos (x) = 0 : x = \frac{π}{2} + 2 πn, x = \frac{3 π}{2} + 2 πn

cos (x) = - 1 : x = π + 2 πn

cos (x) = 1 : x = 2 πn

Combine all the solutions

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

2 cos (x) = 1

sin (2 x) sin (x) = cos (x)

2 sec^{2} (x) + tan^{2} (x) - 3 = 0

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

csc (x) + cot (x) = 1

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