find the solutions of the equation that are in the interval [0,2pi/3) cos3u +cos6u=0

Answer 1

Let θ = 3u

cos θ + cos 2θ = 0

cos θ + cos² θ - sin² θ = 0

cos θ + cos² θ - (1 - cos² θ) = 0

2cos² θ + cos θ - 1 = 0

(2cos θ - 1)(cos θ + 1) = 0

2cos θ = 1

cos θ = 1/2θ

θ = π/3 or 5π/3

u = π/9 or 5π/9

cos θ = -1

θ = π

u = π/3