JEE Main & Advanced Sample Paper JEE Main Sample Paper-26

  • question_answer
    The area of a triangle ABC is equal to\[({{a}^{2}}+{{b}^{2}}-{{c}^{2}})\], where a, b and c are the sides of the triangle. The value of tan C equals

    A)  1                    

    B)  2

    C)  3                                

    D)  4

    Correct Answer: D

    Solution :

    \[\cos C=\frac{{{a}^{2}}+{{b}^{2}}-{{c}^{2}}}{2ab}\] Now \[\Delta ={{a}^{2}}+{{b}^{2}}-{{c}^{2}}\] Hence \[\cos C=\frac{\Delta }{2ab}\]                   ?(1) Also \[\Delta =\frac{1}{2}ab\sin C\Rightarrow \,\frac{2\Delta }{\sin C}=ab\] \[\Rightarrow \,\sin C=\frac{2\Delta }{ab}\] \[\therefore \] From (1) and (2), we get \[\tan C=\frac{2\Delta }{ab}.\,\frac{2ab}{\Delta }=4\]

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