Question

Which of the following is true?

• A. $tan|ta{n}^{-1}x|=|x|$
• B. $cot|co{t}^{-1}x|=|x|$
• C. $ta{n}^{-1}|tanx|=|x|$
• D. $sin|si{n}^{-1}x|=|x|$

Answer 1

The correct option is A $tan|ta{n}^{-1}x|=|x|$

$|ta{n}^{-1}x|=ta{n}^{-1}x,if0\le x<\frac{\pi }{2}=-ta{n}^{-1}x,if-\frac{\pi }{2}<x<0butta{n}^{-1}|x|=ta{n}^{-1}x,ifx>0=ta{n}^{-1}x,ifx<0\therefore |ta{n}^{-1}x|=ta{n}^{-1}|x|\Rightarrow tan\left(ta{n}^{-1}\right(|x|\left)\right)=|x|$