Question

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

• A. $-\pi$
• B. $+\pi$
• C. $-2\pi$
• D. $+2\pi$

Answer 1

Answer: (B)

$+\pi$

The value of ${\sin }^{-1}x+{\sin }^{-1}\frac{1}{x}+{\cos }^{-1}x+{\cos }^{-1}\frac{1}{x}$ is defined only when $x,\frac{1}{x}ϵ[-1,1]$

which is possible only when $x=\pm 1$

For which ${\sin }^{-1}x+{\sin }^{-1}\frac{1}{x}+{\cos }^{-1}x+{\cos }^{-1}\frac{1}{x}=\pi$