A) \[{{\cot }^{-1}}x\]
B) \[\pi +{{\cot }^{-1}}x\]
C) \[\pi -{{\cot }^{-1}}x\]
D) \[-\pi +{{\cot }^{-1}}x\]
Correct Answer: D
Solution :
\[x>0{{\cot }^{-1}}x=t\] |
\[t\in \left( \frac{\pi }{2},\,\,\pi \right)\] |
\[\cot \,\,t=x\] |
\[\tan \,\,t=\frac{1}{x}\] |
\[{{\tan }^{-1}}\tan ={{\tan }^{-1}}\frac{1}{x}\] |
\[t-\pi ={{\tan }^{-1}}\frac{1}{x}\] |
\[-\pi +{{\cot }^{-1}}x={{\tan }^{-1}}\frac{1}{x}.\] |
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