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Prove cos(A+B)cos(A-B)=Cos^2A+cos^2B-1
To prove this trigonometric equation, use the sum difference rule of trigonometric identities and then simplify:
cos(A+B)=cosAcosB-sinAsinB
cos(A-B)=cosAcosB+sinAsinBTherefore, cos(A+B)cos(A-B) =(cosAcosB-sinAsinB)(cosAcosB+sinAsinB)=cos^2Acos^2B-sin^2Asin^2B=cos^2B(1-sin^2A)-sin^2A(1-cos^2B)=cos^2B-cos^2Bsin^2A-sin^2A+cos^2Bsin^2A=cos^2B-sin^2A=cos^2B-(1-cos^2A)=cos^2A+cos^2B-1=R.H.SHence, proof
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