1. The problem is to simplify the expression $2\sin 25^\circ \cos 25^\circ$. 2. We use the double-angle identity for sine: $$\sin 2\theta = 2 \sin \theta \cos \theta$$ 3. Here, $\theta = 25^\circ$, so: $$2 \sin 25^\circ \cos 25^\circ = \sin (2 \times 25^\circ) = \sin 50^\circ$$ 4. Therefore, the simplified form of the expression is $\sin 50^\circ$. This means the original expression equals the sine of 50 degrees.