## Trigonometry (11th Edition) Clone

The statement $$\cos70^\circ\cos20^\circ-\sin70^\circ\sin20^\circ=0$$ is true.
$$\cos70^\circ\cos20^\circ-\sin70^\circ\sin20^\circ=0$$ 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.