# How do you simplify #csc^2(θ) / (1 + tan^2(θ) )#?

##### 2 Answers

#### Explanation:

Let's see, we have:

In this case, I would probably start by rewriting everything in terms of sines and cosines, since we know that

and

So we now have:

Here, I notice that the denominator can be simplified if I would multiply it by

and if I multiply

Opening the parentheses, this becomes:

which is our famous identity and is

Yes. The denominator becomes 1 if I would multiply by

So let's do the following:

We can do this since any number over itself (except zero) is equal to 1.

So provided that

Now, we know the denominator becomes 1, and we are left with just the "top":

where

Simplify:

Ans:

#### Explanation:

Use the trig identity: