A) 1
B) 2
C) \[\frac{\sqrt{3}}{2}\]
D) \[\sqrt{3}\]
Correct Answer: D
Solution :
[d] \[\frac{\cos A}{a}=\frac{\cos B}{b}=\frac{\cos C}{c}\] \[\Rightarrow \frac{\cos A}{2R\sin A}=\frac{\cos B}{2R\sin B}=\frac{\cos C}{2R\sin C}\] \[\Rightarrow \cot A=\cot B=\cot C\] \[\Rightarrow A=B=C=60{}^\circ \Rightarrow \Delta ABC\] is equilateral Hence, \[\Delta =\frac{\sqrt{3}}{4}{{a}^{2}}=\sqrt{3}.\]
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