Answer
$\dfrac {\sin ^{4}\alpha -\cos ^{4}\alpha }{\sin ^{2}\alpha -\cos ^{2}\alpha }=1$
Work Step by Step
$\dfrac {\sin ^{4}\alpha -\cos ^{4}\alpha }{\sin ^{2}\alpha -\cos ^{2}\alpha }=\dfrac {\left( \sin ^{2}\alpha -\cos ^{2}\alpha \right) \left( \sin ^{2}\alpha +\cos ^{2}\alpha \right) }{\left( \sin ^{2}\alpha -\cos ^{2}\alpha \right) }=\sin ^{2}\alpha +\cos ^{2}\alpha =1$
