Let I = ∫ d x cos ⁡ x - sin ⁡ x 2 = 1 f x + C (where, C is the constant of integration). If f π 3 = 1 - 3 , then the number of solution(s) of f x = 2020 in x ∈ π 2 , π is/are

Step-by-step solution

I = ∫ sec 2 ⁡ x 1 - tan ⁡ x 2 d x Let tan ⁡ x = t ⇒ sec 2 ⁡ x d x = d t ⇒ I = ∫ d t 1 - t 2 = ∫ 1 - t - 2 d t ⇒ I = 1 1 - t + C = 1 1 - tan ⁡ x + C ∴ f x = 1 - tan ⁡ x If f x = 2020 ⇒ 1 - tan ⁡ x = 2020 ⇒ tan ⁡ x = - 2019 Which happens once in x ∈ π 2 , π