A) \[x\,\in R\]
B) \[x\,\in (-\infty ,\,1)\]
C) \[x\,\in (-1,\,\,\infty )\]
D) \[x\,\in (-\,\infty ,-1)\]
Correct Answer: B
Solution :
Given that, \[{{\tan }^{-1}}\left( \frac{1+x}{1-x} \right)=\frac{\pi }{4}+{{\tan }^{-1}}x\] \[RHS=\frac{\pi }{4}+{{\tan }^{-1}}x\] \[={{\tan }^{-1}}+{{\tan }^{-1}}x\] \[={{\tan }^{-1}}\left( \frac{1+x}{1-x} \right),\] if \[x<1\] \[\therefore \] \[x\,\,\in \,\,(-\infty ,\,\,1)\]
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