Limit question. Have solution, need to know how to get it.

[bored2death97]

Homework Statement

I was working on a problem in my book, and I didn't know how to answer the question. So I looked at the solution manual. and it had this

http://imgur.com/VF4yl

I do not know where the (cosx + 1) on the bottom came from. Any ideas? Please explain.

Homework Equations

sin(x+y)= sinx cosy + cosx siny

The Attempt at a Solution

I get the top part though, you factor out the 2, multiply the cos and sin then it becomes sin(x+y) sort of thing.Ok, nevermind, I am sorry, I didn't realize they factored out the cosx-1 and then multiplied by (cosx +1)/(cosx+1) So I got it now.

 

[Mark44]

Homework Statement

I was working on a problem in my book, and I didn't know how to answer the question. So I looked at the solution manual. and it had this

http://imgur.com/VF4yl

I do not know where the (cos-1) on the bottom came from. Any ideas? Please explain.

They multiplied by 1 in the form
$$ \frac{cos(x) + 1}{cos(x) + 1}$$

Homework Equations

sin(x+y)= sinx cosy + cosx siny

One that is relevant to the question you asked is:
sin²(x) + cos²(x) = 1

The Attempt at a Solution

I get the top part though, you factor out the 2, multiply the cos and sin then it becomes sin(x+y) sort of thing.