Answer
$$\sin(2\pi-x)=-\sin x$$
Work Step by Step
$$\sin(2\pi-x)$$
Here we can use the identity that we have proved in Exercise 36:
$$\sin(A-B)=\sin A\cos B-\cos A\sin B$$
Therefore:
$$\sin(2\pi-x)=\sin2\pi\cos x-\cos2\pi\sin x$$
$$\sin(2\pi-x)=0\times\cos x-1\times\sin x$$
$$\sin(2\pi-x)=-\sin x$$
