How do I simplify this inequality

[MeMoses]

Homework Statement

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)

Homework Equations

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

 

[SammyS]

Homework Statement

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)

Homework Equations

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

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).

 

[MeMoses]

Thanks, that's all I needed