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In DeltaABC,("cos"^(2)(A)/(2))/(a)+("cos...

In `DeltaABC,("cos"^(2)(A)/(2))/(a)+("cos"^(2)(B)/(2))/(b)+("cos"^(2)(C)/(2))/(c)` is equal to

A

`(s^(2))/(2abc)`

B

`(s^(2))/(abc)`

C

`(s^(2))/(3abc)`

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
B
We have `("cos"^(2)(A)/(2))/(a)+("cos"^(2)(B)/(2))/(b)+("cos"^(2)(C)/(2))/(c)`
`={((s(s-a))/(bc))/(a)}+{((s(s-b))/(ca))/(b)}+{((s(s-c))/(ab))/(c)}`
`=(s(s-a+s-b+s-c))/(abc)=(s[3s-(a+b+c)])/(abc)`
`=(s(3s-2s))/(abc)=(s^(2))/(abc)`
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