For an acute angle A it is given that $\sin A+{\sin }^{2}A=1$.
Find the value of ${\cos }^{2}A+{\cos }^{4}A$.

From $\sin A+{\sin }^{2}A=1$ we get $\sin A=1-{\sin }^{2}A={\cos }^{2}A$. Substituting, ${\cos }^{2}A+{\cos }^{4}A=\sin A+(\sin A{)}^2=\sin A+{\sin }^{2}A=1$. Solving numerically instead (sin A is about 0.618) gives the same 1, but takes far longer. The trap is assuming the "cos version" must be the opposite of the "sin version" and answering 0.