- OK, so, ladies and gentlemen, what we're going to do is we want to simplify this expression. By simplifying the expression, what we want to do is try to write it as one trigonometric term or an evaluation. So what we're going to do when looking at this is right now, I have cotangent of theta times secant of theta. And what I want to look at, Lauren, is see how can I maybe rewrite this so I might be able to simplify. 

So when we're looking on our page 344, we say, what are the different ways that we can transform these expressions? And by using the reciprocal identity, there's a couple of things you can do with this. So we look at, how can I rewrite cotangent? And a lot of you will say, well, cotangent of theta, by using the reciprocal identity, is 1 over tangent of theta. And also, cotangent of theta, by using the quotient identity, is going to be cosine of theta over sine of theta. 

So there's two different ways we talked about how we can transform or how we can rewrite cotangent. Secant of theta, just by using the reciprocal identity, we can say that the secant of theta is equal to 1 over cosine theta. So let's transform here cotangent and secant and see if we can change it up or simplify it somehow. So if I just both use the reciprocal identities in both of these, let's see if that happens. Let's see what that'll do. 

So rather than writing cotangent theta, I can write 1 divided by cotangent theta, right? They're equal to each other. That's what I was getting to you guys last class period without speaking. I was saying they're equal to each other, so you can rewrite them using the other term. So if I did this and then I rewrote secant as 1 over cosine of theta, am I really doing anything that's going to simplify this right at this point? No. I mean, I transformed it, but this isn't really going to help me out at all. 

So let's maybe try-- my eraser. Let's maybe try rather than using the reciprocal identity for cotangent, let's try using the quotient identity. It still equals cotangent. Now, when I do it like when I change it by using the quotient identity, what I notice is when I multiply across, my cosines are going to divide out to 1, leaving me with 1 over sine of theta, which leaves me with cosecant of theta. 

Does that make a little sense for what I did? All right, so when you guys are simplifying, you want to look at, what are your identities that you can use to transform your equation or your expression or your terms that will help you maybe to divide or multiply out to get you 1, to simplify it down to one single expression or one single Function?