If in `DeltaABC,(cosA)/(a)=(cosB)/(b)=(cosC)/(c) and ` side a=2, then the area of the triangle is

Options

A. 1
B. 2
C. `(sqrt(3))//2`
D. `sqrt(3)`

Answer

D

Explanation

`because(cosA)/(a)=(cosB)/(b)=(cosC)/(c)`
`therefore(cosA)/(KsinA)=(cosB)/(KsinB)=(cosC)/(KsinC)`
`impliescotA=cotB=cotC`
`impliesA=B=C=60^(@)`
`becauseDeltaABC` is equilateral with a=2
`thereforeDelta=(sqrt(3))/(4)a^(2)=(sqrt(3))/(4)(2)^(2)=sqrt(3)`