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

Question

Let S = x &#8712; - &#960; , &#160; &#960; : x &#8800; 0 , &#160; &#177; &#960; 2 . The sum of all distinct solution of the equation 3 sec &#8289; x + c o s e c &#160; x + 2 tan &#8289; x - cot &#8289; x = 0 , in the set S is equal to

Aicharya · Accepted Answer

3 Cosx + 1 Sinx + 2 Sinx cosx - Cosx sinx = 0 3 sin &#8289; x + cos &#8289; x = 2 cos &#8289; 2 x &#8658; cos &#8289; 2 x = cos &#8289; x - &#960; 3 &#8658; 2 x = 2 n &#960; &#177; x - &#960; 3 , 2 x = 2 n &#960; + x &#8722; &#960; 3 2 x = 2 n &#960; &#8722; x + &#960; 3 &#8658;&#160;x = 6 n - 1 &#960; 3 or 6 n + 1 &#960; 9 &#8658; x = &#160; - &#960; 3 , &#960; 9 , 7 &#960; 9 and - 5 &#960; 9 in - &#960; , &#160; &#960; &#160; &#8658; s u m &#160; = &#160; 0

Let S = x ∈ - π ,   π : x ≠ 0 ,   ± π 2 . The sum of all distinct…

Solution

Let S = x &#8712; - &#960; , &#160; &#960; : x &#8800; 0 , &#160; &#177; &#960; 2 . The sum of all distinct…

Solution

Let S = x ∈ - π , π : x ≠ 0 , ± π 2 . The sum of all distinct…