1. **State the problem:** Simplify the expression $2(1 - \sin A)(\cos A)$. 2. **Recall the distributive property:** $a(b+c) = ab + ac$. We will apply this to expand the product. 3. **Expand the expression:** $$2(1 - \sin A)(\cos A) = 2[(1)(\cos A) - (\sin A)(\cos A)] = 2(\cos A - \sin A \cos A)$$ 4. **Distribute the 2:** $$2 \cos A - 2 \sin A \cos A$$ 5. **Final simplified form:** $$2 \cos A - 2 \sin A \cos A$$ This is the simplified expression. You can factor further if needed, but this is the expanded and simplified form.