If the expression ( 1 + tan ⁡ x + tan 2 ⁡ x ) ( 1 - cot ⁡ x + cot 2 ⁡ x ) is positive, then the complete set of values of x is

Step-by-step solution

(1 + tan ⁡ x + tan 2 ⁡ x ) ( 1 + t a n 2 x - tan ⁡ x ) tan 2 ⁡ x > 0 ⇒   1 + tan 2 ⁡ x 2 - tan 2 ⁡ x tan 2 ⁡ x > 0 Since, 1 + tan 2 ⁡ x > tan 2 ⁡ x ,   ∀ x ∈ R - x = n π 2 ,   n ∈ I Hence, given expression is positive for all values of x ∈ R - x = n π 2 ,   n ∈ I