A) \[0\]
B) \[1\]
C) \[\frac{1}{\sqrt{3}}\]
D) \[\sqrt{3}\]
Correct Answer: C
Solution :
\[cs{{o}^{1}}\frac{(1-{{x}^{2}})}{(1+{{x}^{2}})}+{{\tan }^{-1}}x=\frac{\pi }{2}\] \[\Rightarrow \] \[2{{\tan }^{-1}}x+{{\tan }^{-1}}x=\frac{\pi }{2}\] \[\Rightarrow \] \[3{{\tan }^{-1}}x=\frac{\pi }{2}\] \[\Rightarrow \] \[{{\tan }^{-1}}x=\frac{\pi }{6}\] \[\Rightarrow \] \[x=\tan \frac{\pi }{6}\] \[\Rightarrow \] \[x=\frac{1}{\sqrt{3}}\]
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