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

Step-by-step solution

cot x ⋅ cos x − cot x + cos x − 1 = 0 ⇒ cot ⁡ x + 1 cos ⁡ x - 1 = 0 ⇒ cot ⁡ x = - 1 or cos ⁡ x = 1 (Not possible as sin ⁡ x ≠ 0 ) Hence, 2 solutions are possible in 0 , 2 π