A) \[\pi \]
B) \[\frac{\pi }{2}\]
C) \[\frac{3\pi }{2}\]
D) None of these
Correct Answer: A
Solution :
\[{{\sin }^{-1}}x+{{\sin }^{-1}}\frac{1}{x}+{{\cos }^{-1}}x+{{\cos }^{-1}}\frac{1}{x}\] = \[\{{{\sin }^{-1}}(x)+{{\cos }^{-1}}(x)\}+\left\{ {{\sin }^{-1}}\left( \frac{1}{x} \right)+{{\cos }^{-1}}\left( \frac{1}{x} \right) \right\}\] \[=\frac{\pi }{2}+\frac{\pi }{2}=\pi \].
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