Solve the equation for x if 0 ≤ x < 2π. Give your answer in radians using exact values only. (Enter your answers as a comma-separated list.) cos x + cos 2x = 0

Question

Solve the equation for x if 0 ≤ x < 2π. Give your answer in radians using exact values only. (Enter your answers as a comma-separated list.)

cos x + cos 2x = 0

Answer 1

cos 2x + cos x = 0

cos²x - sin^2x + cos x = 0

2cos²x + cosx - 1 = 0

cos x = -1 and cos x = 1/2

There are only 3 values which work in the specified interval:π, π/3 and 5π/6