#### Answer

$$\cos40^\circ\cos50^\circ-\sin40^\circ\sin50^\circ=0$$

#### Work Step by Step

$$\cos40^\circ\cos50^\circ-\sin40^\circ\sin50^\circ$$
Remember the identity cosine of a sum:
$$\cos(A+B)=\cos A\cos B-\sin A\sin B$$
That means we can shorten the exercise as follows:
$$\cos40^\circ\cos50^\circ-\sin40^\circ\sin50^\circ=\cos(40^\circ+50^\circ)$$
$$\cos40^\circ\cos50^\circ-\sin40^\circ\sin50^\circ=\cos90^\circ$$
$$\cos40^\circ\cos50^\circ-\sin40^\circ\sin50^\circ=0$$