If $\sec^{-1}x = \operatorname{cosec}^{-1}y, \text{ then find the value of } \cos^{-1}\frac{1}{x} + \cos^{-1}\frac{1}{y}$ …

Problem

\sec^{-1}x = \operatorname{cosec}^{-1}y, \text{ then find the value of } \cos^{-1}\frac{1}{x} + \cos^{-1}\frac{1}{y}