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In a Delta ABC, a =2b and |A-B| =(pi)/(3...

In a `Delta ABC, a =2b and |A-B| =(pi)/(3).` Determine the `angleC.`

A

`pi/4`

B

`pi/3`

C

`pi/6`

D

none of these

Text Solution

Verified by Experts

We ave,
`a=2brArragtbrArrAgtb`
`thereforeabs(A-B)=pi/3rArrA-B=pi/3`
Now,
`(a-b)/(a+b)cotC/2=tan((A-B)/2)`
`rArr1/3cotC/2=tan(pi)/6`
`rArrcotC/2=sqrt3rArrC/2=pi/6rArrC=pi/3`
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