Ta có:
$\begin{array}{l}\dfrac{sin\alpha}{tan\alpha + cot\alpha}\\ = \dfrac{sin\alpha}{\dfrac{sin\alpha}{cos\alpha}+\dfrac{cos\alpha}{sin\alpha}}\\ =\dfrac{sin\alpha}{\dfrac{sin^2\alpha+cos^2\alpha}{sin\alpha.cos\alpha}}\\ = sin\alpha.sin\alpha.cos\alpha\\ =sin^2\alpha.cos\alpha\\ = (1 - cos^2\alpha)cos\alpha\\ =cos\alpha - cos^3\alpha\end{array}$
