Question

If $\alpha ={\log }_e\sqrt{\cot \frac{\pi }{12}}$, then find the value of ${\left(\frac{\sum _{k=0}^{\infty }{e}^{-2ka}}{\sum _{k=0}^{\infty }(-1{)}^k{e}^{-2k\alpha }}\right)}^2$

Answer 1

Answer: 3

Correct answer is (c)