PUC trigonometry multiple angles?

Question

prove that sin4Acos2A / (1+cos4A)(1+cos2A) = tanA

Answer 1

Best Answer - Chosen by Asker

Consider,
sin4Acos2A / (1+cos4A)(1+cos2A)
= 2sin2A cos^2 2A / (1+cos4A)(1+cos2A)..[cos4A=cos^2 2A-sin^2 2A]
= 2sin2A cos^2 2A / (1+cos^2 2A - sin^2 2A)(1+cos2A)
= 2sin2A cos^2 2A / (cos^2 2A + cos^2 2A)(1+cos2A)
= 2sin2A cos^2 2A / 2cos^2 2A (1+cos2A)
= sin2A/(1+cos2A)
= 2sinAcosA/2 cos^2 A
= sinA/cosA
= tanA
I hope the steps are easy to understand.

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Asker's Comment:

thnx