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

Question

If 0 &#160; &#8804; x &#60; 2 &#960; , 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

Aicharya · Accepted Answer

2 cos 2 x cos x + 2 cos 3 x cos x = 0 &#8658; 2 cos x cos 2 x + cos 3 x = 0 2 cos x 2 cos 5 x 2 cos x 2 = 0 x = &#960; 2 , 3 &#960; 2 , &#160; &#960; , &#960; 5 , 3 &#960; 5 , 7 &#960; 5 , 9 &#960; 5 7 &#160; Solutions.

If 0 &#160; &#8804; x &#60; 2 &#960; , then the number of real values of x , which satisfy the equation cos…

Solution

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