# Homework Help: How do I simplify this inequality

1. Sep 16, 2012

### MeMoses

1. The problem statement, all variables and given/known data
So i'm following along with my physics book and I get to the point where
Mg * abs(sin(θ) - cos(θ)) <= μMg * (cos(θ) + sin(θ)
Next they say: If tan(θ) >= 1 then
sin(θ) - cos(θ) <= μ(cos(θ) + sin(θ)) => tan(θ) <= (1+μ) / (1-μ)

2. Relevant equations

3. The attempt at a solution
How do I go from sin(θ) - cos(θ) <= μ(cos(θ) + sin(θ)) to tan(θ) <= (1+μ) / (1-μ)?
Could someone walk me through this or at least get me started? Thanks

2. Sep 16, 2012

### SammyS

Staff Emeritus
You get to do most of the walking. (Hopefully, you know by now that that's how we do things here at PF.)

Take
$\sin(\theta) - \cos(\theta) \le \mu(\cos(\theta) + \sin(\theta))$​
and divide both sides by cos(θ) .

Simplify, and the only trig function remaining is tan .

Now, try to isolate tan(θ).

3. Sep 16, 2012

### MeMoses

Thanks, that's all I needed