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Question
If `(cos^4α)/(cos^2β) + (sin^4α)/(sin^2β)` = 1, prove that sin4α + sin4β = 2 sin2α sin2β
Solution
`(cos^4alpha)/(cos^2beta) + (sin^4alpha)/(sin^2beta)` = 1
`(cos^4alpha sin^2beta + sin^4alpha cos^2beta)/(cos^2beta sin^2beta)` = 1
(1 – sin2α)2 sin2β + sin4α (1 – sin2β) = sin2β cos2β
(1 – 2sin2α + sin4α) sin2β + sin4α – sin4α sin2β
= sin2β (1 – sin2β) sin2β – 2sin2α + sin2β + sin4α sin2β + sin4α sin4α sin2β
= sin2β – sin4β
sin4α + sin4β = 2 sin2α sin2β
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