# simplifying the trigonometric expression $\frac{\cot\theta - \tan\theta}{\sin\theta + \cos\theta} + \frac{1}{\cos\theta}$

I'm stuck on this expression for which I don't have any answer. $$\frac{\cot\theta - \tan\theta}{\sin\theta + \cos\theta}+\frac{1}{\cos\theta}$$ Need some help on the simplifying steps.

Here is what I get from a calculator

• To better assist you please indicate what you have tried so far and where you are getting stuck. This allows people to better tailor their answer to your skill level. Additional then people won't complete and say that this isn't a homework site. – Ian Miller Nov 22 '15 at 16:41
• @IanMiller I need to simplify it – BsD Nov 22 '15 at 16:43
• You do realize none of this will prepare you for your upcoming test? – Ian Miller Nov 22 '15 at 16:48
• Find a common denominator, and go from there. It's as simple as it seems youtube.com/watch?v=1Rx2gj-vDms – John Joy Nov 22 '15 at 21:26

If you let $\cos\theta$ be $c$ and $\sin\theta$ be $s$ then you have: $$\frac{\frac{c}{s}-\frac{s}{c}}{s+c}+\frac{1}{c}=\frac{\frac{c^2}{s}-s+s+c}{(s+c)c}=\frac{\frac{cs+c^2}{s}}{sc+c^2} =\frac{cs+c^2}{s(cs+c^2)}=\frac{1}{s}$$ or it can be simplifed to: $$\frac{1}{\sin\theta}$$
$$\frac{c/s- s/c}{s+c}+\frac{1}{c}= ( c-s)/s c + ...$$