Read the Formula Backwards

Read from right to left, the formulas collapse a sum of products into one function. That finds exact values for angles that are not special themselves.

Take $\cos\left(80^{\circ}\right)\cos\left(20^{\circ}\right)+\sin\left(80^{\circ}\right)\sin\left(20^{\circ}\right)$. Neither 80° nor 20° has an exact value you know, but the shape is cos A cos B + sin A sin B, the right side of cos(A - B). So it equals $\cos\left(80^{\circ}-20^{\circ}\right)$, which is $\cos\left(60^{\circ}\right)$, and that is 1/2.

Match the shape before the numbers: which functions pair up, and which sign joins them. cos cos with a plus is cos(A - B); cos cos with a minus is cos(A + B); sin cos plus cos sin is sin(A + B).