Cos y/ 1-sin y= 1+sin y/cos y. verify the identity. show all steps!

When proving identities, the answer is in the explanation.

Step-by-step explanation:

I have two terms in this denominator here.

I also know that by Pythagorean Identity.  

So I don't know how comfortable you are with multiplying this denominator's conjugate on top and bottom here but that is exactly what I would do here.  There will be other problems will you have to do this.

Big note here: When multiplying conjugates all you have to do is multiply fist and last.  You do not need to do the whole foil.  That is when you are multiplying something like , the result is just .

Let's do that here with our problem in the denominator.

In that last step, I apply the Pythagorean Identity I mentioned way above.

Now You have a factor of cos(y) on top and bottom, so you can cancel them out.  What we are really saying is that cos(y)/cos(y)=1.

This is the desired result.

We are done.