Question

Find the value of ${\sin }^{-1}x+{\sin }^{-1}\frac{1}{x}+{\cos }^{-1}x+{\cos }^{-1}\frac{1}{x}$

Answer 1

$\begin{array}{c}\Rightarrow {\sin }^{-1}x+{\cos }^{-1}x+{\sin }^{-1}\frac{1}{x}+{\cos }^{-1}\frac{1}{x}\\ \Rightarrow \left({\sin }^{-1}x+{\cos }^{-1}x\right)+\left({\sec }^{-1}x+\cos e{c}^{-1}x\right)\\ \frac{\pi }{2}+\frac{\pi }{2}=\pi \end{array}$

Hence, this is the answer.