Let S = (x ∈ (- , ) :x 0 , 2) The sum of all distinct solutions of the equation 3sec x + cosec x + 2(tan x – cot x) = 0 in the set S is equal to

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Correct answer: C. (c) 3secx + cosecx + 2 (tanx – cotx) = 0⇒ 3 sinx + cosx + 2 (sin2x – cos2x ) = 0 3 sinx + cosx – 2cos2x = 0 ⇒ sin (x+ 3) = cos2x cos (π/3 – x) = cos2x ⇒ 2x = 2nπ ± (π/3 – x) x = 2 nπ3+ 9 or x = 2nπ – 3. – 100^o – 60 o + 20 o +140 o = 0

$Let S = (x \in (- π, π) : x \neq = 0, \pm \frac{π}{2}) The sum of all distinct solutions of the equation 3 sec x + cosec x + 2(tan x - cot x) = 0 in the set S is equal to$

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