Discussion

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.

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