Question

Prove that sin6 θ + cos6 θ + 3sin2 θ cos2 θ = 1

Answer 1

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${sin}^{6} θ + {cos}^{6} θ + 3 {sin}^{2} θ {cos}^{2} θ \times 1 \\ = {sin}^{6} θ + {cos}^{6} θ + 3 {sin}^{2} θ {cos}^{2} θ ( {sin}^{2} θ + {cos}^{2} θ) \\ = { {(sin}^{2} θ)}^{3} + { {(cos}^{2}θ) }^{3} + 3 {sin}^{2} θ {cos}^{2} θ ( {sin}^{2} θ + {cos}^{2} θ) \\ = {( {sin}^{2}θ \: + {cos}^{2}θ) }^{3} \\ = {1}^{3} \\ = 1 \\ \large\bold\red{Hence \: Proved } \\ \huge \fcolorbox{black}{cyan}{♛Hope it helps U♛}$

Answer 2

Answer:

answer is 1...........