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In a A B C if b+c=3a ,t h e ncotB/2dotc...

In a ` A B C` if `b+c=3a ,t h e ncotB/2dotcotC/2` has the value equal to: `` 4 b. 3 c. 2 d. 1

A

`4`

B

`3`

C

`2`

D

`1`

Text Solution

Verified by Experts

The correct Answer is:
C
In `a Delta ABC if b + c = 3a` …………
`cot.(B)/(2).cot.(C )/(2)=(s(s-b))/(Delta)(s(s-c))/(Delta)((s-a))/(s-a) = (s)/(s-a)`
`= (2s)/(2s-2a)`
but `a+b+c = 4a implies 2s = 4a` Hence `cot. (B)/(2). cot. (C )/(2)`
`= (4a)/(2a) = 2I`
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