8. Prove that sin^6 A + cos^6 A = 1-3 sin^2A Cos^2A
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sin^6A + cos^6A
= (sin^2A)3 + (cos^2A)3
= (sin^2A + cos^2A)(sin^4A – sin^2Acos^2A + cos^4A)
= 1 (sin^4A – sin^2Acos^2A + cos^4A + 2sin^2Acos^2A – 2sin^2Acos^2A)
= (sin2A + cos2A) – 3sin2Acos2A
= 1 – 3sin^2Acos^2A
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