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If $\cos A + \cos^2 A = 1$, then find the value of $\sin^2 A + \sin^4 A$.
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$\cos A + \cos^2 A = 1 \Rightarrow \cos A = 1 - \cos^2 A = \sin^2 A$
$\therefore \sin^2 A + \sin^4 A = \cos A + \cos^2 A (\because \sin^2 A = \cos A)$
$= 1$
$\therefore \sin^2 A + \sin^4 A = \cos A + \cos^2 A (\because \sin^2 A = \cos A)$
$= 1$