The total number of solutions of the equation sin ⁡ x tan ⁡ 4 x = cos ⁡ x for all x ∈ 0 , π are

Step-by-step solution

tan ⁡ 4 x = cot ⁡ x = tan ⁡ π 2 - x 4 x = n π + π 2 - x 5 x = n π + π 2 = 2 n + 1 π 2 ⇒ x = 2 n + 1 π 10 x = π 10 , 3 π 10 , 5 π 10 , 7 π 10 , 9 π 10 Hence, 5 solutions in 0 , π