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In DeltaABC, prove that: a(cosC-cosB)=...

In `DeltaABC`, prove that:
`a(cosC-cosB)=2(b-c)cos^(2)A/2`

Text Solution

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LHS `=a(cosC-cosB)`
`k.sinC.2sin(C+B)/(2).sin(B-C)/(2)`
`=k.2sinA/2cosA/2.2sin(pi-A)/(2).sin(B-C)/(2)`
`=k.2sin(pi-(B+C))/(2)sin(B-C)/(2). cosA/2.2cosA/2`
`=k.(2cos(B+C)/(2).sin(B-C)/(2)).2cos^(2)A/2`
`=2k. (sinB-sinC).cos^(2)A/2`
`=2(b-c).cos^(2)A/2=`RHS Hence Proved.
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