we know that
[tex]\cos (\theta-\varphi)=\cos \theta\cos \varphi+\sin \theta\cos \varphi[/tex]
Now, we have to find every value in the formula using the identities.
Now, substitute the values in the formula:
[tex]\begin{gathered} \cos (\theta-\varphi)=\cos \theta\cos \varphi+\sin \theta\sin \varphi \\ =\frac{-12}{13}\times\frac{-15}{17}+\frac{-5}{13}\times\frac{8}{17} \\ =\frac{180}{221}-\frac{40}{221} \\ =\frac{140}{221} \end{gathered}[/tex]
Thus, the correct answer is 140/221.
