The value of ∑ 1/ sin(π/4+ (k-1)π/6) sin (π/4 + kπ/6) ; ∈ k =1 , 13 is equal to

Question

The value of \(\displaystyle\sum_{k=1}^{13} \) \(\cfrac{1}{sin(\frac{\pi}{4}+\frac{(k-1)\pi}{6})sin(\frac{\pi}{4}+\frac{k\pi}{6})}\) is equal to

(A) 3 - √3

(B) 2(3 - √3)

(C) 2(√3 - 1)

(D) 2(2+ √3)

Answer 1

Correct option is (C) 2(√3 - 1)