#### Answer

$$\cos(90^\circ+\theta)=-\sin\theta$$

#### Work Step by Step

$$A=\cos(90^\circ+\theta)$$
Here we need to use the cosine sum identity:
$$\cos(A+B)=\cos A\cos B-\sin A\sin B$$
Applying that identity to $A$:
$$A=\cos90^\circ\cos\theta-\sin90^\circ\sin\theta$$
$$A=0\times\cos\theta-1\times\sin\theta$$
$$A=-\sin\theta$$