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KVPY Sample Paper KVPY Stream-SX Model Paper-30

  • question_answer
    In a triangle ABC, angle 8 < angle C and the values of B & C satisfy the equation \[2\tan x-k(1+{{\tan }^{2}}x)=0\] where \[(0<k<1)\]. Then the measure of angle A is:

    A) \[\pi /3\]

    B) \[2\pi /3\]

    C) \[\pi /2\]

    D) \[3\pi /4\]

    Correct Answer: C

    Solution :

    \[2\tan x-k(1+ta{{n}^{2}}x)=0\,\,;\,\,0<k<1\]
    Since \[\angle B\]and \[\angle C\]of a \[\Delta ABC\] satisfy it
    \[\therefore \tan C+\tan B\,\,are\,\,roots\]\[\therefore \,\,\,\tan C+\tan B=\frac{2}{K}\] and \[\tan C\tan B=1\]
    \[\Rightarrow \]\[\tan (C+B)=\frac{\tan C+\tan B}{1-\tan C\tan B}=\frac{\frac{2}{k}}{1-1}\]\[\Rightarrow B+C=\frac{\pi }{2}\,\,\,\,\therefore \,\,\,\,\,A=\frac{\pi }{2}\]


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