The number of solutions of equation, sin 5 x cos 3 x = sin 6 x cos 2 x , in the interval 0 , π are

Step-by-step solution

Given, sin 5 x cos 3 x = sin 6 x cos 2 x The given equation can be written as 2 sin 5 x cos 3 x = 2 sin 6 x cos 2 x ⇒ sin 8 x + sin 2 x = sin 8 x + sin 4 x ;   ∵ 2 sin A cos B = sin A + B + sin A - B ⇒ sin 2 x - sin 4 x = 0 ⇒ - 2 sin x cos 3 x = 0 , Hence, sin x = 0 or cos 3 x = 0 . x = n π n ∈ I or 3 x = k π + π 2 k ∈ I Therefore, since x ∈ 0 , π , the given equation is satisfied, x = 0 ,   π ,   π 6 ,   π 2 or 5 &#960