Answer
$$\sin^3\theta+\cos^3\theta=(\cos\theta+\sin\theta)(1-\cos\theta\sin\theta)$$
The trigonometric expression is an identity.
Work Step by Step
$$\sin^3\theta+\cos^3\theta=(\cos\theta+\sin\theta)(1-\cos\theta\sin\theta)$$
We take on the left side first.
$$A=\sin^3\theta+\cos^3\theta$$
As following the expansion, $$a^3+b^3=(a+b)(a^2-ab+b^2)$$
$A$ is now becoming
$$A=(\sin\theta+\cos\theta)(\sin^2\theta-\sin\theta\cos\theta+\cos^2\theta)$$
$$A=(\sin\theta+\cos\theta)[(\sin^2\theta+\cos^2\theta)-\sin\theta\cos\theta]$$
$$A=(\sin\theta+\cos\theta)(1-\sin\theta\cos\theta)$$ (as $\sin^2\theta+\cos^2\theta=1$)
That means the left and right sides are equal. The trigonometric expression is hence an identity.
