Asked by Halle
Trig Identity Prove:
cos(x+y)cos(x-y)=cos^2(x)+cos^2(y)-1
cos(x+y)cos(x-y)=cos^2(x)+cos^2(y)-1
Answers
Answered by
drwls
Use the formulas for cos (x+y) and cos(x-y):
cos(x+y) = cosx cosy - sinx siny
cos(x-y) = cosx cosy + sinx siny
The product of the two is
cos^2x cos^2y - sin^2x sin^2y
= cos^2x cos^2y -(1-cos^2x)(1-cos^2y)
= cos^2x cos^2y -(1-cos^2x)(1-cos^2y)
You finish it off.
cos(x+y) = cosx cosy - sinx siny
cos(x-y) = cosx cosy + sinx siny
The product of the two is
cos^2x cos^2y - sin^2x sin^2y
= cos^2x cos^2y -(1-cos^2x)(1-cos^2y)
= cos^2x cos^2y -(1-cos^2x)(1-cos^2y)
You finish it off.
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