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In a DeltaABC , if a b and c are in AP ,...

In a `DeltaABC` , if a b and c are in AP ,then the value of `("sin"(A)/(2)"sin"(C)/(2))/("sin"(B)/(2))` is

A

1

B

`(1)/(2)`

C

2

D

`-1`

Text Solution

Verified by Experts

The correct Answer is:
B
Since , a b and c are in AP .
`rArr2b =a+crArr3b =2s`
`rArrs=(3b)/(2)`
Now , `("sin"(A)/(2)"sin"(C)/(2))/("sin"(B)/(2))=sqrt((ac(s-b)(s-c)(s-b)(s-a))/((s-a)(s-c)xxbcxxab))`
`=(s-b)/(b)=((3b)/(2)-b)/(b)=(1)/(2)`
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