Why $\cos a\cdot \cos b+\sin a\cdot \sin b = \cos (b-a)$

Question

I do not get why

$$\cos a\cdot \cos b+\sin a\cdot \sin b = \cos (b-a)$$

Thank you for your help

Answer 1

The following diagram by Blue demonstrates this perfectly:

Hence, we conclude

$$\cos(a\pm b) = \cos a\cos b\mp \sin a\sin b$$

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