Question

6. If sin⁴θ + sin²θ = 1, then the value of cos²θ + cos⁴θ is​

Answer 1

${sin}^{4} \theta + {sin}^{2} \theta = 1 \\ {sin}^{4} \theta = 1 - {sin}^{2} \theta \\ {sin}^{4} \theta = {cos}^{2} \theta ...(1) \\ \\ Now \: \: \: \: {cos}^{2} \theta + {cos}^{4} \theta \\ = {sin}^{4} \theta + {sin}^{8} \theta \: \: \: \: \:[ from \: \: (1)] \\ = {sin}^{2} \theta( {sin}^{2} \theta + {sin}^{4} \theta ) \\ = {sin}^{2} \theta$