\(\sin\alpha+\cos\alpha=m\Leftrightarrow\left(\sin\alpha+\cos\alpha\right)^2=m^2\)
\(\sin^2\alpha+\cos^2\alpha+2\sin\alpha\cdot\cos\alpha=m^2\)
\(\Leftrightarrow2\sin\alpha\cdot\cos\alpha=m^2-1\)
\(\Leftrightarrow\sin\alpha\cdot\cos\alpha=\frac{m^2-1}{2}\)