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Matrices and Determinants question

2017 · 8 Apr · Shift 1 · Q36

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JEE Main
Mathematics
Matrices and Determinants
2017 · 8 Apr · Shift 1 · Q36

Matrices and Determinants question

2017 · 8 Apr · Shift 1 · Q36

JEE MainMathematicsMatrices and DeterminantsMCQ+4 / −1

If

S = \left\{ {x \in \left[ {0,2\pi } \right]:\left| {\begin{matrix} 0 & {\cos x} & { - \sin x} \\ {\sin x} & 0 & {\cos x} \\ {\cos x} & {\sin x} & 0 \\ \end{matrix} } \right| = 0} \right\},

then

\sum\limits_{x \in S} {\tan \left( {{\pi \over 3} + x} \right)}

is equal to :

A
$4 + 2\sqrt 3$
B
$- 2 + \sqrt 3$
C
$- 2 - \sqrt 3$
D
$-\,\,4 - 2\sqrt 3$

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