I'm revising for an exam and I'm stuck on part of my revision question.

I have proven that $\displaystyle Tan\theta=\frac{5sin\alpha}{13-5cos\alpha}$ in the given question, but now I have to prove that $\displaystyle tan\theta$ has the greatest value at $\displaystyle cos\alpha=\frac{5}{13}$

Can anyone help me prove it?