[JEE Advanced 2016] 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
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) $\frac{5\pi}9$
1 Answer
VAVidaara Admin
✓ Vidaara Team
✓ Accepted
· 1mo 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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