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In DeltaABC , the value of (cotA/2cotB/...

In `DeltaABC` , the value of `(cotA/2cotB/2-1)/(cotA/2cotB/2)` is

A

`(a)/(a+b+c)`

B

`(c)/(a+b+c)`

C

`(2a)/(a+b+c)`

D

`(2c)/(a+b+c)`

Text Solution

Verified by Experts

The correct Answer is:
D
`("cot"(A)/(2)"cot"(B)/(2)-1)/("cot"(A)/(2)"cot"(B)/(2))=1-"tan"(A)/(2)"tan"(B)/(2)`
`=1-sqrt(((s-b)(s-c))/(s(s-a)))sqrt(((s-a)(s-c))/(s(s-b)))`
`=1-(s-c)/(s)=(c)/(s)`
`=(2c)/(a+b+c)`
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