Answer
$$\sin100^\circ\cos10^\circ-\cos100^\circ\sin10^\circ=1$$
Work Step by Step
$$X=\sin100^\circ\cos10^\circ-\cos100^\circ\sin10^\circ$$
Recall the sine difference identity that
$$\sin A\cos B-\cos A\sin B=\sin(A-B)$$
Looking back at $X$, we find $X$ is indeed the above identity with $A=100^\circ$ and $B=10^\circ$.
Therefore, we can rewrite $X$ as
$$X=\sin(100^\circ-10^\circ)$$
$$X=\sin90^\circ$$
$$X=1$$
In conclusion, $$\sin100^\circ\cos10^\circ-\cos100^\circ\sin10^\circ=1$$
