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Prove that: sin(45^(@)-A)sin(45+A)=1/2...

Prove that:
`sin(45^(@)-A)sin(45+A)=1/2cos2A`

Text Solution

Verified by Experts

LHS `=sin(45^(@)+A).sin(45^(@)-A)`
`=1/2[2sin(45^(@)+A).sin(45^(@)-A)]`
`=1/2[cos(45^(@)+A)-(45^(@)-A)-cos(45^(@)+A)+(45^(@)-A)]`
`=1/2[cos2A-cos90^(@)]`
`=1/2(cos2A=0)`
`=1/2cos2A`= RHS Hence proved.
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