jee-advanced 2016 Q39

jee-advanced · India · paper2 Addition & Double Angle Formulae Telescoping Sum of Trigonometric Terms
The value of $\sum _ { k = 1 } ^ { 13 } \frac { 1 } { \sin \left( \frac { \pi } { 4 } + \frac { ( k - 1 ) \pi } { 6 } \right) \sin \left( \frac { \pi } { 4 } + \frac { k \pi } { 6 } \right) }$ is equal to
(A) $3 - \sqrt { 3 }$
(B) $2 ( 3 - \sqrt { 3 } )$
(C) $2 ( \sqrt { 3 } - 1 )$
(D) $2 ( 2 + \sqrt { 3 } )$ 
The value of $\sum _ { k = 1 } ^ { 13 } \frac { 1 } { \sin \left( \frac { \pi } { 4 } + \frac { ( k - 1 ) \pi } { 6 } \right) \sin \left( \frac { \pi } { 4 } + \frac { k \pi } { 6 } \right) }$ is equal to\\
(A) $3 - \sqrt { 3 }$\\
(B) $2 ( 3 - \sqrt { 3 } )$\\
(C) $2 ( \sqrt { 3 } - 1 )$\\
(D) $2 ( 2 + \sqrt { 3 } )$
Paper Questions
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