prove that
cos(A+B)*cos(A-B) = cos2A-sin2B
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Answer:
cos(A+B)cos(A-B)=
(cosAcosB-sinAsinB)(cosAcosB+sinAsinB)
(a-b)(a+b)=a^2-b^2
(cosAcosB)^2-(sinAsinB)^2
cos^2Acos^2B-sin^2Asin^2B
cos^2A(1-sin^2B)-(1-cos^2A)sin^2B
cos^2A-cos^2Asin^2B-sin^2B+cos^2Asin^2B
cos(A-B)cos(A+B)=cos^2A-sin^2B
=(1-sin^2A)-(1-sin^2B)
=cos^2B-sin^2A
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