Question

How to do this question by proving the identity?

Answer 1

$\sin^3 \theta-\cos^3 \theta=(\sin \theta-\cos \theta)(\sin \theta\cos \theta+1)\\\\ (\sin \theta-\cos \theta)(\sin^2 \theta+\sin \theta\cos \theta +\cos^2 \theta)=(\sin \theta-\cos \theta)(\sin \theta\cos \theta+1)\\\\ (\sin \theta-\cos \theta)(\sin \theta\cos \theta+1)=(\sin \theta-\cos \theta)(\sin \theta\cos \theta+1)$