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Question
Prove that: sin4 θ + cos4θ = 1 - 2sin2θ cos2 θ.
Solution
LHS = (sin2θ)2 + (cos2 θ)2 + 2 sin2θ cos2θ - 2 sin2θ cos2θ
= ( sin2θ + cos2θ )2 - 2 sin2θ cos2θ
= 1 - 2 sin2θ cos2θ
= RHS
Hence proved.
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