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JAMIA MILLIA ISLAMIA Jamia Millia Islamia Solved Paper-2010

  • question_answer
        In a\[\Delta ABC,\]if \[\frac{\cos A}{a}=\frac{\cos B}{b}=\frac{\cos C}{c}\]and the side\[a=2,\]then area of the triangle is

    A)  1                                            

    B)  2

    C)  \[\frac{\sqrt{3}}{2}\]                                    

    D)  \[\sqrt{3}\]

    Correct Answer: D

    Solution :

                    \[\frac{\cos A}{a}=\frac{\cos B}{b}=\frac{\cos C}{c}\] \[\Rightarrow \]               \[\frac{\cos A}{k\sin A}=\frac{\cos B}{k\sin B}=\frac{\cos C}{k\sin C}\]                                                                 (by Sine rule) \[\Rightarrow \]               \[\cot A=\cot B=\cot C\] \[\Rightarrow \]               \[A=B=C=60{}^\circ \] \[\therefore \]\[\Delta ABC\]is equilateral. Thus, area\[\Delta ABC=\frac{\sqrt{3}}{4}{{(side)}^{2}}\]                                 \[=\frac{\sqrt{3}}{4}.4=\sqrt{3}\]


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