Simplify Trigonometry expression

1. Jul 10, 2016

Eagertolearnphysics

1. The problem statement, all variables and given/known data
I want to know how he simplified this expression to tan (theta)

2. Relevant equations

3. The attempt at a solution

2. Jul 10, 2016

Fightfish

Hint: How is $\tan \theta$ related to $\sin \theta$ and $\cos \theta$?

3. Jul 10, 2016

Eagertolearnphysics

I know it's Sin/Cos however, I don't know how he did it.

4. Jul 10, 2016

Fightfish

So how do you get $\sin \theta / \cos \theta$ from the original expressions?

5. Jul 10, 2016

cnh1995

Are you familiar with the componendo-dividendo property of equal ratios?
If a/b=c/d, then (a+b)/(a-b)=(c+d)/(c-d).

Last edited: Jul 10, 2016
6. Jul 10, 2016

Eagertolearnphysics

I really would like to thank you guys I got it. I was hesitating to post the question as I thought it was too obvious. Thanks again

7. Jul 11, 2016

James R

In case somebody else reading this didn't get the answer, we can take an expression like this:

$\sin \theta - \cos \theta \le \mu (\cos \theta + \sin \theta)$

and divide both sides by $\cos \theta$ to get

$\tan \theta - 1 \le \mu (1 + \tan \theta)$

then go from there.