Let S = x ∈ - π , π : x ≠ 0 , ± π 2 . The sum of all distinct solution of the equation 3 sec ⁡ x + c o s e c x + 2 tan ⁡ x - cot ⁡ x = 0 , in the set S is equal to

Step-by-step solution

3 Cosx + 1 Sinx + 2 Sinx cosx - Cosx sinx = 0 3 sin ⁡ x + cos ⁡ x = 2 cos ⁡ 2 x ⇒ cos ⁡ 2 x = cos ⁡ x - π 3 ⇒ 2 x = 2 n π ± x - π 3 , 2 x = 2 n π + x − π 3 2 x = 2 n π − x + π 3 ⇒ x = 6 n - 1 π 3 or 6 n + 1 π 9 ⇒ x =   - π 3 , π 9 , 7 π 9 and - 5 π 9 in - π ,   π   ⇒ s u m   =   0