Question

tan2 theta - sin2 theta = tan2 theta, sin2 theta​

Answer 1

${tan}^{2} \theta - {sin}^{2} \theta \\ \\ = \frac{ {sin}^{2} \theta}{cos ^{2} \theta} - {sin}^{2} \theta \\ \\ = \frac{ {sin}^{2} \theta - {sin}^{2} \theta \: {cos}^{2} \theta}{ {cos}^{2} \theta } \\ \\ = \frac{ {sin}^{2} \theta(1 - {cos}^{2} \theta) }{ {cos}^{2} \theta} \\ \\ = \frac{ {sin}^{2} \theta \: {sin}^{2} \theta }{ {cos}^{2} \theta} \\ \\ = {tan}^{2} \theta \: {sin}^{2} \theta$