Inverse Trigonometric Functions Question 119
$ f(x)=\tan^{-1}x+\tan^{-1}( \frac{1}{x} );g(x)=\sin^{-1}x+\cos^{-1}x $ are identical functions if
Options:
A) $ x\in R $
B) $ x>0 $
C) $ x\in [-1,1] $
D) $ x\in (0,1] $
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Answer:
Correct Answer: D
$ ( \frac{\pi }{2}-2x )=\cos 6x= \begin{matrix} \frac{\pi }{2}x>0 \\ \frac{-\pi }{2}x<0 \\ \end{matrix} . $
$ {{\sin }^{-1}}x+{{\cos }^{-1}}x=\frac{\pi }{2}\forall x\in [-1,1] $ .
BETA
