A) \[\pi \]
B) \[2\pi \]
C) \[\frac{\pi }{2}\]
D) \[\frac{3\pi }{2}\]
Correct Answer: D
Solution :
\[{{\sin }^{-1}}x+{{\sec }^{-1}}x+{{\cot }^{-1}}x+{{\cos }^{-1}}x\] \[+\text{cose}{{\text{c}}^{-1}}\,x+{{\tan }^{-1}}\,x\] \[=({{\sin }^{-1}}\,x+{{\cos }^{-1}}x)+({{\sec }^{-1}}x+\text{cose}{{\text{c}}^{-1}}x)\] \[+({{\tan }^{-1}}x+{{\cot }^{-1}}x)\] \[=\frac{\pi }{2}+\frac{\pi }{2}+\frac{\pi }{2}\] \[=\frac{3\pi }{2}\]
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