[tex]\tan \alpha +\dfrac{1}{\tan \alpha}=\dfrac{7}{2}\\\\\dfrac{\sin \alpha}{\cos \alpha} +\dfrac{\cos \alpha}{\sin \alpha}=\dfrac{7}{2}\\\\\dfrac{\sin^2 \alpha}{\sin \alpha\cos \alpha} +\dfrac{\cos^2 \alpha}{\sin \alpha\cos \alpha}=\dfrac{7}{2}\\\\\dfrac{\sin^2 \alpha+\cos^2 \alpha}{\sin \alpha\cos \alpha}=\dfrac{7}{2}\\\\\dfrac{1}{\sin \alpha\cos \alpha}=\dfrac{7}{2}\\\\7\sin \alpha\cos \alpha=2\\\\\sin \alpha\cos \alpha=\dfrac{2}{7}[/tex]
