Trig idents while computing limit

[quicksilver123]

My screenshots show an attempt at a solution and the given solution path from the book, but I can't seem to figure it out.

 

[scottdave]

I was able to work through that step using $$cos(x+y)=cos(x)cos(y)-sin(x)sin(y)$$ and $$sin(x+y)=sin(x)cos(y)+cos(x)sin(y)$$
See this link:

http://www.mathwords.com/t/trig_identities.htm

 

[quicksilver123]

That is the identity I used to expand the (x+h) terms but could not factor to the next step due to the sin(h) term... unless I made an error in my expansion that I haven't caught?

 

[scottdave]

In your work, factor a sin(x) from the first 2 terms and cos(x) from the next 2 terms. You should now have the same as the solution guide. Note that it takes 2 lines to display theirs. I don't know what you've done in the denominator, though. .

 

[quicksilver123]

Thanks. I don't know why I didn't see that.