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Question
Prove that sin2 θ + cos4 θ = cos2 θ + sin4 θ.
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Solution
L.H.S. = sin2 θ + cos4 θ
= 1 - cos2 θ + cos4 θ
= 1 - cos2 θ (1 - cos2 θ)
= 1 - (1 - sin2 θ) sin2 θ
= 1 - sin2 θ + sin4 θ
= cos2 θ + sin4 θ
= R.H.S.
Hence proved.
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