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If in a !ABC , a =2b ,and abs(A-B)=(pi)/...

If in a `!ABC` , a =2b ,and `abs(A-B)=(pi)/3` then C =

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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