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 $$\begin{align*} &\frac{\sin\cos(\sin^2+\cos^2)}{\sin+\cos}\\ &\frac{\sin\cos(1)}{\sin+\cos} \end{align*}$$
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 $$\begin{align*} &\frac{\sin\cos(\sin^2+\cos^2)}{\sin+\cos}\\ &\frac{\sin\cos(1)}{\sin+\cos} \end{align*}$$