Question

Sin4-cos4=sin2-cos2 please find the answer for this question

Answer 1

Hey

$To \: Prove: \: \\ \\ sin {}^{4} \alpha - \cos {}^{4} \alpha = \sin {}^{2} - \cos {}^{2} \alpha \ \\ \\ LHS \\ \\ sin {}^{4} \alpha - \cos {}^{4} \alpha \\ \\ = ( \sin {}^{2} \alpha + \cos {}^{2} \alpha )( \sin {}^{2} \alpha - \cos {}^{2} \alpha ) \\ \\ = \sin {}^{2} \alpha - \cos {}^{2} \alpha = RHS$