The number of solutions of the equation cos x + π 3 cos π 3 - x = 1 4 cos 2 2 x , x ∈ - 3 π , 3 π is:

Step-by-step solution

Given, cos x + π 3 cos x - π 3 = 1 4 cos 2 2 x ⇒ 2 cos x + π 3 cos x - π 3 = 1 2 cos 2 2 x ⇒ cos 2 x + cos 2 π 3 = 1 2 cos 2 2 x ⇒ cos 2 x + - 1 2 = 1 2 cos 2 2 x ⇒ cos 2 2 x - 2 cos 2 x + 1 = 0 ⇒ cos 2 x - 1 2 = 0   or   cos 2 x = 1 ⇒ 2 x = - 6 π , - 4 π , - 2 π , 0 , 2 π , 4 π , 6 π So, x ∈ - 3 π , - 2 π , - π , 0 , π , 2 π , 3 π So total 7 solutions.