prove that tan^2A - tan^2 B = (sin^2 A - sin^2 B)/cos^2 A. cos^2 B
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Step-by-step explanation:
tan2A - tan2B
= sin2A /cos2A - sin2B/cos2B
= (sin2Acos2B - cos2Asin2B)/cos2Acos2B
= {sin2A(1-sin2B) - (1-sin2A)sin2B}/cos2Acos2B
= (sin2A - sin2Asin2B - sin2B + sin2Asin2B)/cos2Acos2B
= (sin2A - sin2B)/cos2Acos2B
= RHS proved
[note: sin2A is sin^2A and cos2A is cos^2A]
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