find all SOLUTIONS of the following equation in the interval [0,2π)

Question

cosx=cos3x

Answer 1

cosx=cos3x

Using trignometric multiple angle formula

cosx=4 cos^3 (x) - 3cos x

4 cos^3 (x) - 3cos x-cosx=0

4 cos^3 (x) - 4cos x=0

4cosx(cos^2x-1)=0

cosx=0   or cos^2x-1=0

cosx=0

x=90 or 270

cos^2x-1=0

cosx=+1 or -1

x=0,360

x=0,90,270,360

Comments

The solutions of the given equation are x = 0, x = π/2, and x = π on the interval [0, 2π).