Question

(cos⁶theta +sin⁶theta )+3 sin²thetacos²theta
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Answer 1

$({cos}^{6} \theta + {sin}^{6} \theta) + 3 {sin}^{2} \theta \: {cos}^{2} \theta \\ = ( {cos}^{2} \theta) ^{3} + ( { {sin}^{2} \theta})^{3} + 3 {sin}^{2} \theta \: {cos}^{2} \theta \\ = ( {cos}^{2} \theta + {sin}^{2} \theta)( {cos}^{4} \theta + {sin}^{4} \theta - {sin}^{2} \theta {cos}^{2} \theta) + 3 {sin}^{2} \theta {cos}^{2} \theta \\ = {cos}^{4} \theta + {sin}^{4} \theta + 2 {sin}^{2} \theta {cos}^{2} \theta \\ = ( { {sin}^{2} \theta + {cos}^{2} \theta})^{2} \\ = 1$