Question

Prove that : sin⁴θ - Cos⁴θ = 1-2cos²θ​

Answer 1

Step-by-step explanation:

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