Giải thích các bước giải:

Ta có:

$P=\dfrac{\sin^3\alpha+\cos^3\alpha}{\sin\alpha-\cos\alpha}$

$\to P=\dfrac{\sin^3\alpha+\cos^3\alpha}{(\sin\alpha-\cos\alpha)\cdot 1}$

$\to P=\dfrac{\sin^3\alpha+\cos^3\alpha}{(\sin\alpha-\cos\alpha)\cdot (\sin^2\alpha+\cos^2\alpha)}$

$\to P=\dfrac{(\sin^3\alpha+\cos^3\alpha):\sin^3\alpha}{(\sin\alpha-\cos\alpha)\cdot (\sin^2\alpha+\cos^2\alpha):\sin^3\alpha}$

$\to P=\dfrac{1+\dfrac{\cos^3\alpha}{\sin^3\alpha}}{(1-\dfrac{\cos\alpha}{\sin\alpha})\cdot (1+\dfrac{\cos^2\alpha}{\sin^2\alpha})}$

$\to P=\dfrac{1+\cot^3\alpha}{(1-\cot\alpha)(1+\cot^2\alpha)}$

$\to P=\dfrac{1+(-3)^3}{(1-(-3))(1+(-3)^2)}$

$\to P=\dfrac{-13}{20}$