The number of solutions of the equation 1 + sin 4 x = cos 2 3 x , x ∈ - 5 π 2 , 5 π 2 is:

Step-by-step solution

The given trigonometric equation can be written as 1 - c o s 2 3 x + s i n 4 x = 0 ⇒   s i n 2 3 x + s i n 4 x = 0 ⇒ s i n 3 x = 0 and s i n x = 0 ,   x ∈ - 5 π 2 , 5 π 2   In given interval s i n x = 0 at x = - 2 π ,   - π ,   0 ,   π ,   2 π and these values are also satisfied by s i n 3 x = 0 . Hence total number of solutions is 5 .