The number of solutions in the interval 0 , π of the equation sin 3 ⁡ x cos ⁡ 3 x + sin ⁡ 3 x cos 3 ⁡ x = 0 is equal to

Step-by-step solution

The given equation can be written as 3 sin ⁡ x - sin ⁡ 3 x 4 cos ⁡ 3 x + sin ⁡ 3 x 3 cos ⁡ x + cos ⁡ 3 x 4 sin ⁡ x cos 3 x ⁡ + cos ⁡ x sin ⁡ 3 x = 0 So, sin ⁡ x + 3 x = 0 ⇒ sin ⁡ 4 x = 0 ⇒ x = n π 4 ,   n ∈ Z . ⇒ x = 0 , π 4 , π 2 , 3 π 4 , π ⇒ 5 solutions