Prove that sin^6 θ + cos^6 θ + 3 sin^2 θ cos^2 θ = 1
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Answer:
LHS = (sin^2 θ)^3 + (cos^2 θ)^3 + 3 sin^2 θ cos^2 θ
= (sin^2 θ + cos^2 θ)^3
= 1^3 = 1 = RHS
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