Question

Let $f\left(x\right)={\cot }^{-1}x+cs{c}^{-1}x$. Then $f\left(x\right)$ is real for

• A. $xϵ[-1,1]$
• B. $xϵ(-\infty ,-1)\bigcup [1,\infty )$
• C. $xϵ(-\infty ,\infty )$
• D. $xϵ(0,\pi )$

Answer 1

The correct option is D $xϵ(0,\pi )$

$f\left(x\right)={\cot }^{-1}\left(x\right)+{\cos }^{-1}\left(x\right)$

$(-\infty ,\infty )(0,\pi )$

$f\left(x\right)\Rightarrow (0,\pi )$