Proving the greatest value for Tan

**thepopasmurf** · December 8th 2008, 04:52 AM

I'm revising for an exam and I'm stuck on part of my revision question.
I have proven that $Tan\theta=\frac{5sin\alpha}{13-5cos\alpha}$ in the given question, but now I have to prove that $tan\theta$ has the greatest value at $cos\alpha=\frac{5}{13}$
Can anyone help me prove it?

**mr fantastic** · December 8th 2008, 04:56 AM

Originally Posted by thepopasmurf

I'm revising for an exam and I'm stuck on part of my revision question.
I have proven that $Tan\theta=\frac{5sin\alpha}{13-5cos\alpha}$ in the given question, but now I have to prove that $tan\theta$ has the greatest value at $cos\alpha=\frac{5}{13}$
Can anyone help me prove it?

Use calculus to find the maximum of $y = \frac{5sin\alpha}{13-5cos\alpha}$ :

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

**thepopasmurf** · December 8th 2008, 05:02 AM

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

**thepopasmurf** · December 8th 2008, 10:45 AM

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

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