Step-by-step explanation:
cos(3x) − 3 cos x = cos(2x) + 1
Use triple and double angle formulas.
(4 cos³x − 3 cos x) − 3 cos x = (2 cos²x − 1) + 1
Simplify.
4 cos³x − 6 cos x = 2 cos²x
4 cos³x − 2 cos²x − 6 cos x = 0
2 cos³x − cos²x − 3 cos x = 0
Factor.
cos x (2 cos²x − cos x − 3) = 0
cos x (cos x + 1) (2 cos x − 3) = 0
Solve.
cos x = 0 → x = 90°, 270°
cos x + 1 = 0 → x = 180°
2 cos x − 3 = 0 → no solution
