Posted by Momo on .
Solve this equation algebraically:
(1sin x)/cos x = cos x/(1+sin x)

I know the answer is an identity, and when graphed, it looks like cot x. I just don't know how to get there. I tried multiplying each side by its conjugate, but I still feel stuck. This is what I have so far:
cos^2(x)/cos x + sin x =
cos x  sin x/cos^2(x)
...but I'm not really sure how to get to the answer. Help please?
Thank you!

Math 
jim,
Do you mean solve it or prove it?
It is an identity, so there really isn't a specific solution: it's true for all x.
I suggest you try reformatting as
(1sin x)/cos x  cos x/(1+sin x) = 0
Then bring both fractions to the common denominator (cosx)(1+sinx), and I think you'll recognise the numerator you're left with! 
Math 
Momo,
Ok, I worked it out, and so far i have this:
cos^2x  cos x  sinxcosx /
cosx + sinxcosx
Now I just need some help with reducing? 
Math 
jim,
Um, no. Wrong turn somewhere. It's a LOT simpler than that.
Your numerator will be :
(1sinx)(1+sinx)  cos^2x