Question

Solve the equation . cos2x−cosx=0. on the interval [0,2π)

Answer 1

cos 2x = 2cos^2(x) − 1
2cos^2 (x) − 1 − cos(x) ≡ 2cos^2(x) − cos(x) − 1
Let cos(x) = y
2y^2 − y − 1
(2y + 1) (y − 1) y = −1/2
y = 1
y = cos(x)
∴ cos(x) = −1/2 ; cos(x) = 1
x = 2/3 π ; x = 0
solutions;x = 2/3 π, x = 0, x = 4/3 π, x = 2π