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JEE Main & Advanced Mathematics Triangles & Properties of Triangle Question Bank Self Evaluation Test - Properties of Triangles and Height & Dstances

  • question_answer
    In a \[\Delta ABC;\] if \[2\Delta ={{a}^{2}}-{{(b-c)}^{2}}\] then value of \[\tan A=\]

    A) \[-\frac{4}{3}\]

    B) \[\frac{4}{3}\]

    C) \[\frac{8}{15}\]

    D) \[\frac{4}{15}\]

    Correct Answer: B

    Solution :

    [b] \[2\Delta =(a-b+c)(a+b+c)\] \[\Rightarrow 2\Delta =4(s-b)(s-c)\] \[\Rightarrow 2=\sqrt{\frac{s(s-a)}{(s-b)(s-c)}}\Rightarrow \tan \frac{A}{2}=\frac{1}{2}\] \[\therefore \tan A=\frac{2\times \frac{1}{2}}{1-\frac{1}{4}}=\frac{4}{3}\]


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