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

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