Question

Range of the function $f\left(x\right)=\sqrt{|{\sin }^{-1}|\sin x||-{\cos }^{-1}|\cos x|}$, is

• A. $\left\{0\right\}$
• B. $[0,\sqrt{\frac{\pi }{2}}]$
• C. $[0,\sqrt{\pi }]$
• D. none of these

Answer 1

The correct option is A $\left\{0\right\}$

As, we know that
$|{\sin }^{-1}|\sin x||={\cos }^{-1}|\cos x|,\forall xϵ$ domain
$\therefore f\left(x\right)=\sqrt{|{\sin }^{-1}|\sin x||-{\cos }^{-1}|\cos x|}=0,\forall x\in$ domain
$\therefore$ Range of $f\left(x\right)\in \left\{0\right\}$
Hence, (a) is the correct answer.