JEE Main & Advanced Sample Paper JEE Main Sample Paper-38

  • question_answer If \[0<\alpha ,\,\,\beta ,\,\,\gamma <\pi /2\] such that \[\alpha +\beta +\gamma =\frac{\pi }{2}\]and\[\cot \alpha ,\,\,\cot \beta ,\,\,\cot \gamma \] are in arithmetic progression, then the value of \[\cot \alpha \cot \gamma \] is

    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\[\cot \alpha +\cot \gamma =2\cot \beta )\]

adversite


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