I can't understand how to isolate the tan(x) in the Excercise. Can you please show me the passages.
If $\tan{\theta} \geq 1$, then $$ \sin{\theta} - \cos{\theta} \leq \mu (\cos{\theta}+\sin{\theta}) \quad \Rightarrow \quad \tan{\theta} \leq \frac{1+\mu}{1-\mu} $$
Divide by $\cos x$ to get $\tan x -1\leq \mu (1+\tan x)$ or $(tan x)(1-\mu) \leq 1+\mu$. Then divide by $1+\mu$. [Sorry, I wrote $x$ for $\theta$].
(This is valid of $\cos x >0$ and $1+\mu >0$)