# How do you simplify the expression #(cottsec^2t-cott)/(sint tant+cost)#?

##### 1 Answer

#### Explanation:

(I'm writing this bit - the intro - last. I've just worked the problem and I had no idea where it would go or how to simplify it, beyond the fact that I took it apart piece by piece and took substitution opportunities where I could. It's easy to look at something complicated and shrug and think "I can't do this", but if you can start by doing something - anything - you can start to make sense of it. This is not to say that the first few things you do will make the problem simple right away - it can get rather messy. But stick with it and it should resolve itself into something simpler!)

Let's start with the original:

In the numerator, let's factor out

In the numerator, we can use the trig identity

We can substitute in the denominator, using the trig identity