The value of sum(k=1)^(13) (1)/(sin((pi)...

The value of `sum_(k=1)^(13) (1)/(sin((pi)/(4)+((k-1)pi)/(6))sin((pi)/(4)+(kpi)/(6)))` is equals to :

A

`3- sqrt(3)`

B

`2(3- sqrt(3))`

C

`2(sqrt(3)-1)`

D

`2(2+ sqrt(3))`

Verified by Experts

The correct Answer is:

C

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