Answer
$\sin^{2} α$
Work Step by Step
Given expression is-
$\sin^{4} α - \cos^{4} α + \cos^{2} α $
= $\sin^{4} α + \cos^{2} α - \cos^{4} α $
= $\sin^{4} α + \cos^{2} α ( 1 - \cos^{2} α) $
= $\sin^{4} α + \cos^{2} α \sin^{2} α$
( From first Pythagorean identity, $1 - \cos^{2}α$ = $\sin^{2}α$)
= $\sin^{2} α (\sin^{2} α + \cos^{2} α)$
( From first Pythagorean identity, $ \sin^{2}α + \cos^{2}α$ = $1$)
= $\sin^{2} α$
