Answer
The statement $$\cos70^\circ\cos20^\circ-\sin70^\circ\sin20^\circ=0$$ is true.
Work Step by Step
$$\cos70^\circ\cos20^\circ-\sin70^\circ\sin20^\circ=0$$
We examine the left side:
$$X=\cos70^\circ\cos20^\circ-\sin70^\circ\sin20^\circ$$
Remember the cosine sum identity:
$$\cos(A+B)=\cos A\cos B-\sin A\sin B$$
So $X$ is in fact the right side of the above identity with $A=70^\circ$ and $B=20^\circ$.
Therefore, we can simplify $X$:
$$X=\cos(70^\circ+20^\circ)$$
$$X=\cos90^\circ$$
$$X=0$$
That means the statement $$\cos70^\circ\cos20^\circ-\sin70^\circ\sin20^\circ=0$$ is true.
