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what is another form of sin(A+B) sin(A-B)/ cos ^2 A cos^2 B ?show steps

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mathisgay | Student, Undergraduate | Honors

Posted March 15, 2012 at 4:14 AM via web

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what is another form of sin(A+B) sin(A-B)/ cos ^2 A cos^2 B ?

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rcmath | High School Teacher | (Level 1) Associate Educator

Posted March 15, 2012 at 9:03 AM (Answer #1)

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This can be simplified in different ways one way:

`[(sinAcosB+cosAsinB)(sinAcosB-cosAsinB)]/[cos^2Acos^2B]=`

`[sin^2Acos^2B-cos^2Asin^2B]/[cos^2Acos^2B]=`

`[sin^2Acos^2B]/[cos^2Acos^2B]-[cos^2Asin^2B]/[cos^2Acos^2B]=`

`[sin^2A]/[cos^2A]-[sin^2B]/[cos^2B]=`

`tan^2A-tan^2B`

 

 

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