# Thread: Proving the greatest value for Tan

1. ## Proving the greatest value for Tan

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?

2. Originally Posted by thepopasmurf
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?
Use calculus to find the maximum of $\displaystyle y = \frac{5sin\alpha}{13-5cos\alpha}$:

Solve $\displaystyle \frac{dy}{d \alpha} = 0$ etc.

3. I thought about using calculus but I'm fairly sure it can be done without it. The book stays away from calculus until differential equations

4. I'm sorry, but does anyone have any ideas?