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KVPY Sample Paper KVPY Stream-SX Model Paper-2

  • question_answer
    If in a \[\Delta \,ABC,\]\[\tan A+\tan B+\tan C>0,\] then the triangle is

    A) acute - angled    

    B) obtuse - angled

    C) right - angled                 

    D) nothing can be said.

    Correct Answer: A

    Solution :

    \[\tan A+\tan B+\tan \text{ }C=\tan A\tan B\tan C>0\] \[\Rightarrow \] either all of \[\tan A,\]\[\tan B\] & \[\tan C\] are +ve or two are \[-ve.\] But in any triangle two angles are never obtuse \[\therefore \]      \[\tan A,\]\[\tan B,\]\[\tan C>0\]


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