A) \[1\]
B) \[3\]
C) \[{{\cot }^{2}}\beta \]
D) \[\cot \alpha +\cot \gamma \]
Correct Answer: B
Solution :
\[\alpha +\beta +\gamma =\frac{\pi }{2}\Rightarrow \alpha +\gamma =\frac{\pi }{2}-\beta \] so that\[\cot \left( \alpha +\gamma \right)=\cot \left( \frac{\pi }{2}-\beta \right)\] \[\Rightarrow \]\[\frac{\cot \alpha \cot \gamma -1}{\cot \alpha +\cot \gamma }=\frac{1}{\cot \beta }\] \[\Rightarrow \]\[\cot \alpha \cot \gamma -1=2\Rightarrow \cot \alpha \cot \gamma =3\]. (since\[\cot \alpha +\cot \gamma =2\cot \beta )\]
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