Question

The domain of $f\left(x\right)={\sin }^{-1}x+{\cos }^{-1}x+{\tan }^{-1}x+{\cot }^{-1}x$ is

[1 mark]

• A. $R$
• B. $R-[-1,1]$
• C. $[-1,1]$
• D. $(-1,1)$

Answer 1

The correct option is C $[-1,1]$

$f\left(x\right)={\sin }^{-1}x+{\cos }^{-1}x+{\tan }^{-1}x+{\cot }^{-1}x$
We know that the domain of ${\sin }^{-1}x,{\cos }^{-1}x$ is $[-1,1]\cdots \left(i\right)$
and domain of ${\tan }^{-1}x,{\cot }^{-1}x$ is $(-\infty ,\infty )\cdots \left(ii\right)$
From $\left(i\right)\cap \left(ii\right),$ we get
Domain of $f\left(x\right)$ is $[-1,1].$