If … then … is equal to :

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Matrices and Determinants

JEE Main 2017 · 8 Apr, Morning shift · Q4443

MathematicsMedium244×since 2002Q4443

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 :

JEE Main 2017 · 8 Apr, Morning shift · Q4443

MathematicsMedium244×since 2002Q4443

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 :