If \(\sin \theta + \sin^2 \theta = 1\), then the value of \(\cos^2 \theta + \cos^4 \theta\) is:
Answer: B
From the given equation, we can write:
\(\sin \theta = 1 - \sin^2 \theta\)
Using the identity \(\sin^2 \theta + \cos^2 \theta = 1\), we know that \(1 - \sin^2 \theta = \cos^2 \theta\).
Therefore, we have \(\sin \theta = \cos^2 \theta\).
Now we evaluate the expression \(\cos^2 \theta + \cos^4 \theta\). We can write \(\cos^4 \theta\) as \((\cos^2 \theta)^2\).
Substituting \(\cos^2 \theta = \sin \theta\), the expression becomes:
\(\sin \theta + (\sin \theta)^2 = \sin \theta + \sin^2 \theta\)
From the original given equation, we know that \(\sin \theta + \sin^2 \theta = 1\).
So, the value of the expression is 1.