Question

cos(2x)=cos(x)
Hint: start by simplifying with an identity.

Answer 1

cos(2x) = cos(x)

2cos^2(x) -1 = cos(x)

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

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

2cos(x)[cos(x) - 1] + 1[cos(x) - 1] = 0

[cos(x) - 1][2cos(x) + 1] = 0

cosx = 1 or -1/2

x = 0, 2pi , 2pi/3, 4pi/3,