Answer
$$\cos(\theta-270^\circ)=-\sin\theta$$
Work Step by Step
$$A=\cos(\theta-270^\circ)$$
According to the identity of cosine difference:
$$\cos(A-B)=\cos A\cos B+\sin A\sin B$$
$A$ would be:
$$A=\cos\theta\cos270^\circ+\sin\theta\sin270^\circ$$
Remember that $\cos270^\circ=\cos(-90^\circ)=\cos90^\circ=0$, while $\sin270^\circ=\sin(-90^\circ)=-\sin90^\circ=-1$
That means,
$$A=\cos\theta\times0+\sin\theta\times(-1)$$
$$A=-\sin\theta$$
