I am asked to prove the following identities:
I think I should tackle the most complicated side as it is easier to aim for the easier looking side. (hope that makes sense )
I should warn you that I'm not good at this so please excuse my fumbling
I will attempt the RHS, cotθ-tanθ
so I'm stuck! Told you
I was aware of cotθ=1/tanθ=cosθ/sinθ
But I find this a mine field. And never know where to start nor which replacements to use. It's really confusing to me.
I would like to return to this a little later and ask you some questions about your thinking, if I may?
so the LHS has only one thing to play with. So I should tackle this side?
On the right track?
Also thank goodness for LaTeX. It's not that hard to write on paper though
Note that and
Subbing in our double angle identity for \tan wherever occurs:
Looking at the numerator:
Get the same denominator by multipling by
Distribute the and simplify:
Note the similarity of this to the right hand side's numerator. Therefore, leave it like this and work on the denominator
Looking at the denominator (of the overall fraction)
Rewrite 1 as
The second term can be simplified to
Since the two terms now have the same denominator we can combine them:
The numerator of this fraction can be simplified to
As this is also similar to the RHS leave it in this form.
Bringing both parts together
Which makes our fraction equal to
Dividing by a fraction is the same as 'flipping' it (taking the reciprocal) and multiplying.
cancels to leave us with:
Well. That was a rather bigger than expected process.
Thanks for that
Your right - I should learn Latex, and will make an effort to do so after this weekend, which is this coming Monday. Promise Promise.
For anybody reading this who is interested, I just did a search on Latex video tutorials and came up with a couple of sites instantly. It seems there is a lot of help available online, as always.
TechScreencast - LaTeX Intro :: tutorial, videos, articles, screencast to learn technology"
YouTube - Tutorial LaTex
latex video tutorial rapidshare, megaupload, torrent download
Though I haven't looked closely at them, yet, I'm pretty certain they will be helpful and are reputable sites.
Is the last link ok?