Given: $\cos A + \cos^2 A = 1$
$$\Rightarrow \cos A = 1 - \cos^2 A = \sin^2 A$$
Now,
$$\sin^2 A + \sin^4 A = \cos A + (\cos A)^2 = \cos A + \cos^2 A = \mathbf{1}$$
The key step is rewriting the given condition as $\cos A = 1 - \cos^2 A = \sin^2 A$ (using the identity $\sin^2 A + \cos^2 A = 1$). Once you substitute $\sin^2 A = \cos A$, the expression $\sin^2 A + \sin^4 A$ becomes exactly the left-hand side of the given condition, which equals 1. Examiners award marks for the substitution step and the final value.