Precalculus (6th Edition) Blitzer

Once the formula for differences of cosines is verified, the other sum and difference formulas can be verified just by changing the values of angles. Let us take an example, $\cos \left( a-b \right)=\cos a\cos b+\sin a\sin b$ Replace b by -b: $\cos \left( a+b \right)=\cos a\cos b-\sin a\sin b$ Hence, verified.