JEE Main & Advanced Sample Paper JEE Main Sample Paper-47

  • question_answer
    If A, B, C and D are the angles of a quadrilateral, then \[\frac{\sum{\tan \,A}}{\sum{\cot \,A}}\] is equal to

    A)  \[\Pi \,\,\tan \,\,A\]                   

    B)  \[\Pi \,\,\cot \,\,A\]

    C)  \[\Sigma \,{{\tan }^{2}}A\]            

    D)  \[\Sigma \,{{\cot }^{2}}A\]

    Correct Answer: A

    Solution :

      \[\because \]   \[A+B+C+D=2\pi \] or         \[\tan \,(A+B+C+D)=0\] or \[\frac{\Sigma \,\tan \,A-\Sigma \tan \,A\,\tan \,B\,\tan \,C}{1-\Sigma \tan \,A\,\tan \,B+\tan \,A\,\tan \,B\,\tan \,C\,D}=0\] \[\Rightarrow \] \[\Sigma \tan \,A-\Sigma \tan \,A\,\tan \,B\,\tan \,C=0\] \[\Rightarrow \] \[\Sigma \tan \,A=\tan \,A\,\tan \,B\,\tan \,C\,\tan D\,\,\Sigma \cot \,A\] \[\Rightarrow \] \[\frac{\Sigma \,\tan \,A}{\Sigma \cot \,A}=\Pi \,\tan \,A\]

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