<s>[INST] Verify $\frac{\sin^3A + \cos^3A}{\sin A + \cos A} = 1 - \sin A\cos A$ How can I verify the following trigonometric identity?
$$\frac{\sin^3 A + \cos^3 A}{\sin A+\cos A} = 1-\sin A\cos A.$$
My work so far is 
$$\begin{align*}
&\frac{\sin\cos(\sin^2+\cos^2)}{\sin+\cos}\\
&\frac{\sin\cos(1)}{\sin+\cos}
\end{align*}$$
 [/INST] $$
a^3+b^3 = (a+b)(a^2-ab+b^2).
$$
Use that to factor the numerator.
Also, it is not correct to say that $s^3+c^3 = sc(s^2+c^2)$.
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