If $$S = \left\{ {x \in \left[ {0,2\pi } \right]:\left| {\matrix{ 0 & {\cos x} & { - \sin x} \cr {\sin x} & 0 & {\cos x} \cr {\cos x} & {\sin x} & 0 \cr } } \right| = 0} \right\},$$ then $\sum\limits_{x \in S} {\tan \left( {{\pi \over 3} + x} \right)} $ is equal to :

Question

If

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

then $\sum\limits_{x \in S} {\tan \left( {{\pi \over 3} + x} \right)} $ is equal to :

$4 + 2\sqrt 3 $

$ - 2 + \sqrt 3 $

$ - 2 - \sqrt 3 $

$-\,\,4 - 2\sqrt 3 $

Solution

Please login to view the detailed solution steps...

Go to DASH