Trigonometry

If 0 ≤ x < 2π, then the number of real values of x, which satisfy the equation 

cos x + cos 2x + cos 3x + cos 4x = 0 is

  1. 3
  2. 5
  3. 7
  4. 9

Answer

cos x + cos 2x + cos 3x + cos 4x = 0

cos x + cos 3x + cos 2x + cos 6x = 0

2 cos 2x cos x + 2 cos 3x cos x = 0

2 cos x (cos 2x + cos 3x) = 0

4 cos x cos 5x/2 cos x/2 = 0

x = π/2, 3π/2, π/5, 3π/5, π, 7π/5, 9π/5

Total 7 values of x are possible.

The correct option is C.