Simplify Trigonometry expression

[Eagertolearnphysics]

Homework Statement

I want to know how he simplified this expression to tan (theta)

Homework Equations

The Attempt at a Solution

 

[Fightfish]

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

 

[Eagertolearnphysics]

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

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

 

[Fightfish]

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

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

 

[cnh1995]

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

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).

 

[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

 

[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.