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In DeltaABC,a=2band|A-B|=(pi)/(3), the...

In `DeltaABC,a=2band|A-B|=(pi)/(3)`, then `angleC` is equal to

A

`(pi)/(2)`

B

`(pi)/(3)`

C

`(pi)/(4)`

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
B
Since , a=2b …(i)
`rArrangleAgtangleB`
and `|A-B|=(pi)/(3)rArrA-B=(pi)/(3)` …(ii)
By Napier's analogy `[becauseangleAgtangleB]`
`tan((A-B)/(2))=(a-b)/(a+b)"cot"(C)/(2)`
`rArr(1)/(sqrt(3))=(1)/(3) "cot"(C)/(2)`
`rArr"cot "(C)/(2)=sqrt(3)`
`rArr(angleC)/(2)=(pi)/(6)rArrangleC=(pi)/(3)`
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