Mathematics

Problem

Prove that

\frac{1}{2^2} \sec^2 \frac{x}{2} + \frac{1}{2^4} \sec^2 \frac{x}{2^2} + \frac{1}{2^6} \sec^2 \frac{x}{2^3} + \dots \infty = \csc^2 x - \frac{1}{x^2}