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How to prove the equation cos^2(a+b)-sin^2(a-b)=cos2a cos2b

How to prove the equation cos^2(a+b)-sin^2(a-b)=cos2a cos2b

Grade:11

1 Answers

Hemank
35 Points
6 years ago
Theorem::: cos (A+B).cos (A-B)=(cosAcosB-sinAsinB)(cosAcosB+sinAsinB)=cos^2A.cos^2B-sin^2A.sin^2B Now this expression can be further simplified to cos^2A-sin^2BTherefore......cos (A+B)cos (A-B)=cos^2A-sin^B NOW IN UR QUESTION.......cos^2 (A+B)-sin^2 (A-B) can be written as cos (A+B+A-B).cos(A-B-A-B)Which can be reduced to cos2A.cos(-2B)=cos2A.cos2BHENCE, PROVED.

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