The number of solutions of the equation 4 sin 2 x − 4 cos 3 x + 9 − 4 cos x = 0 ; x ∈ − 2 π , 2 π is:

Step-by-step solution

Given: 4 sin 2 x - 4 cos 3 x + 9 - 4 cos x = 0 ⇒ 4 - 4 cos 2 x - 4 cos 3 x + 9 - 4 cos x = 0 ⇒ 4 cos 3 x + 4 cos 2 x + 4 cos x - 13 = 0 ⇒ 4 cos 3 x + 4 cos 2 x + 4 cos x = 13 We know that, - 1 ≤ cos x ≤ 1 So, the maximum value of LHS is 4 + 4 + 4 = 12 But, RHS is 13 . So, no solutions are possible for the given equation.