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.
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.