Answer
$$\sin(270^\circ-\theta)=-\cos\theta$$
Work Step by Step
$$X=\sin(270^\circ-\theta)$$
According to sine difference identity:
$$\sin(A-B)=\sin A\cos B-\cos A\sin B$$
Expand $X$:
$$X=\sin270^\circ\cos\theta-\cos270^\circ\sin\theta$$
*About $\sin270^\circ$ and $\cos270^\circ$
$$\sin270^\circ=\sin(-90^\circ)\hspace{2cm}\cos270^\circ=\cos(-90^\circ)$$
From the Negative-Angle Identities:
$$\sin(-\theta)=-\sin\theta\hspace{2cm}\cos(-\theta)=\cos\theta$$
So, $$\sin270^\circ=-\sin90^\circ=-1\hspace{2cm}\cos270^\circ=\cos90^\circ=0$$
We replace the values just being found back into $X$:
$$X=(-1)\cos\theta-0\sin\theta$$
$$X=-\cos\theta$$
Overall,
$$\sin(270^\circ-\theta)=-\cos\theta$$
