Question

sin6theta ➕ cos6theta=1-2sin2theta. cos2thta​

Answer 1

${sin}^{6} \alpha + {cos}^{6} \alpha \\ = ({ {sin}^{2} \alpha }) ^{3} + ({ {cos}^{2} \alpha })^{3} \\ = ({ {sin}^{2} \alpha + {cos}^{2} \alpha )}^{3} - \\ 3 {sin}^{2} \alpha {cos}^{2} \alpha ( {sin}^{2} \alpha + {cos}^{2} \alpha ) \\ = {1}^{3} - 3 {sin}^{2} \alpha {cos}^{2} \alpha \\ = 1 - {sin}^{2} \alpha {cos}^{2} \alpha$

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