Given that \(\sin \alpha = \tfrac{3}{5}\) and \(\cos \beta = \tfrac{12}{13}\), prove that one possible value of \(\cos(\alpha + \beta)\) is \(\tfrac{33}{65}\) and find all the other possible values.

Review question
# If $\sin \alpha = 3/5, \cos \beta = 12/13$, what's $\cos(\alpha + \beta)$?

Ref: R9740

Given that \(\sin \alpha = \tfrac{3}{5}\) and \(\cos \beta = \tfrac{12}{13}\), prove that one possible value of \(\cos(\alpha + \beta)\) is \(\tfrac{33}{65}\) and find all the other possible values.