• 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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