1. The problem is to understand how the expression $\pi - \pi \sin^2 x$ can be transformed into $\pi \sin^2 x$. 2. Start with the original expression: $$\pi - \pi \sin^2 x$$ 3. Factor out $\pi$ from both terms: $$\pi (1 - \sin^2 x)$$ 4. Recall the Pythagorean identity: $$\sin^2 x + \cos^2 x = 1$$ which implies $$1 - \sin^2 x = \cos^2 x$$ 5. Substitute this identity back into the expression: $$\pi \cos^2 x$$ 6. Therefore, $\pi - \pi \sin^2 x$ simplifies to $\pi \cos^2 x$, not $\pi \sin^2 x$. 7. If the expression is claimed to be $\pi \sin^2 x$, it is incorrect unless there is a misunderstanding or typo. Final answer: $$\pi - \pi \sin^2 x = \pi \cos^2 x$$