JEE Mains · Maths · STD 11 - Trigonometrical equations
If \(S = \left\{ {x \in \left[ {0,2\pi } \right]:\left| {\begin{array}{*{20}{c}}
0&{\cos {\mkern 1mu} x}&{ - \sin {\mkern 1mu} x}\\
{\sin {\mkern 1mu} x}&0&{\cos {\mkern 1mu} x}\\
{\cos {\mkern 1mu} x}&{\sin {\mkern 1mu} x}&0
\end{array}} \right| = 0} \right\},\) then \(\sum\limits_{x \in S} {\tan \left( {\frac{\pi }{3} + x} \right)} \) is equal to
- A \(4 + 2\sqrt 3 \)
- B \(-2 + \sqrt 3 \)
- C \(-2 - \sqrt 3 \)
- D \(-4 - 2\sqrt 3 \)
Answer & Solution
Correct Answer
(C) \(-2 - \sqrt 3 \)
Step-by-step Solution
Detailed explanation
since the given determinant is equal to zera \(\Rightarrow 0(0-\cos x \sin x)-\cos x\left(0-\cos ^{2} x\right)\) \(-\sin x\left(\sin ^{2} x-0\right)=0\) \(\Rightarrow \cos ^{3} x-\sin ^{3} x=0\) \(\Rightarrow \tan ^{3}=1 \Rightarrow \tan x=1\)…
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