The number of solutions of the equation tan ⁡ x sin ⁡ x - 1 = tan ⁡ x - sin ⁡ x ,   ∀ x ∈ 0,2 π is equal to.

Step-by-step solution

tan ⁡ x sin ⁡ x - tan ⁡ x + sin ⁡ x - 1 = 0 ⇒ tan ⁡ x + 1 sin ⁡ x - 1 = 0 ⇒ tan ⁡ x = - 1 or sin ⁡ x = 1 (Not possible as x ≠ π 2 ) Hence, for tan x = - 1 there are 2 solutions in 0 , 2 π