(sinx+cosx)2 = (1/2)2, what is sinx*cosx?

1. Start with the given equation:
(\sin x + \cos x)^2 = \frac{1}{4}

2. Expand the left-side expression:
\sin^2 x + 2 \sin x \cos x + \cos^2 x = \frac{1}{4}

3. Use the Pythagorean identity $\sin^2 x + \cos^2 x = 1$:
1 + 2 \sin x \cos x = \frac{1}{4}

4. Isolate $2 \sin x \cos x$ by subtracting $1$ from both sides:
2 \sin x \cos x = \frac{1}{4} - 1

5. Simplify the right-side expression:
2 \sin x \cos x = \frac{1}{4} - \frac{4}{4} = -\frac{3}{4}

6. Divide by $2$ to solve for $\sin x \cos x$:
\sin x \cos x = -\frac{3}{8}

Answer:
\sin x \cos x = -\frac{3}{8}