Question

Prove that sin^6theta + cos^6 theta +3sin^2 theta cos^2 theta = 1

Answer 1

Answer:

sin²θ + cos²θ = 1

Therefore (sin²θ + cos²θ)³ = 1

or

(sin²θ)³ + (cos²θ)³ + 3sin²θ cos²θ(sin²θ + cos²θ) = 1

or,

sin^6θ + cos^6θ+ 3sin²θ cos²θ = 1

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