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sin^2A+sin^2(A-B)-2sinAcosBsin(A-B)=sin^...

`sin^2A+sin^2(A-B)-2sinAcosBsin(A-B)=sin^2B`

Text Solution

Verified by Experts

LHS
`sin^2 A + sin (A-B) [sin(A-B) - 2sinAcosB]`
`= sin^2 A + sin(A-B)[sinAcos B- cos A sin B - 2sinAcosB]`
`= sin^2A - sin(A-B)[sin AcosB + cosAsinB]`
`= sin^2 A - sin(A-B) sin(A+B)`
`= sin^2A - sin^2 A + sin^2 B`
`= sin^2B=`RHS
Hence proved
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