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Trigonometric Functions and Equations question

2016 · Shift 2 · Q20

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JEE Advanced
Mathematics
Trigonometric Functions and Equations
2016 · Shift 2 · Q20

Trigonometric Functions and Equations question

2016 · Shift 2 · Q20

JEE AdvancedMathematicsTrigonometric Functions and EquationsMCQ+3 / −1

The value of

\sum\limits_{k = 1}^{13} {{1 \over {\sin \left( {{\pi \over 4} + {{\left( {k - 1} \right)\pi } \over 6}} \right)\sin \left( {{\pi \over 4} + {{k\pi } \over 6}} \right)}}}

is equal to

A
$3 - \sqrt 3$
B
$2\left( {3 - \sqrt 3 } \right)$
C
$2\left( {\sqrt 3 - 1} \right)\,\,\,$
D
$2\left( {2 - \sqrt 3 } \right)$

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