Question

please prove the trigonometric equation in attachment.....​

Answer 1

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

= RHS