For S= x∈(-π,π):x 0,± 2, the sum of all distinct solutions of 3sec x+cosecx+2(tan x-cot x)=0 in S is (a) - 7π 9 (b) - 2π 9 (c) 0 (d) 5π 9

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[JEE Advanced 2016] for s x in pi pi x 0 pi 2 the sum of all

VAVidaara Admin Asked 2d ago 0 views 1 answer

For $S=\{x\in(-\pi,\pi):x\ne0,\pm\frac\pi2\}$, the sum of all distinct solutions of $\sqrt3\sec x+\operatorname{cosec}x+2(\tan x-\cot x)=0$ in $S$ is

(a) $-\frac{7\pi}9$
(b) $-\frac{2\pi}9$
(c) $0$
(d) $\frac{5\pi}9$

VAVidaara Admin ✓ Vidaara Team ✓ Accepted · 2d ago ▲ 0

Correct answer: (c) $0$

Reducing to a single trig equation, the solution set in $S$ is symmetric about $0$, so the distinct solutions sum to $0$.

JEE Advanced 2016 · Trigonometry — verified solution by the Vidaara Team.

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