A) \[\alpha +\beta \]
B) \[\alpha -\beta \]
C) \[\frac{1+\alpha \beta }{\alpha +\beta }\]
D) \[\frac{\alpha \beta -1}{\alpha +\beta }\]
Correct Answer: D
Solution :
Given that \[{{\cot }^{-1}}\alpha +{{\cot }^{-1}}\beta ={{\cot }^{-1}}x\] \[\Rightarrow {{\cot }^{-1}}\left( \frac{\alpha \beta -1}{\alpha +\beta } \right)={{\cot }^{-1}}x\Rightarrow x=\frac{\alpha \beta -1}{\alpha +\beta }\].
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