If 0 ≤ x < 2 π , then the number of real values of x , which satisfy the equation cos x + cos 2 x + cos 3 x + cos 4 x = 0 , is

Step-by-step solution

2 cos 2 x cos x + 2 cos 3 x cos x = 0 ⇒ 2 cos x cos 2 x + cos 3 x = 0 2 cos x 2 cos 5 x 2 cos x 2 = 0 x = π 2 , 3 π 2 ,   π , π 5 , 3 π 5 , 7 π 5 , 9 π 5 7   Solutions.