posted by Momo on .
Solve this equation algebraically:
(1-sin 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?
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
(1-sin 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!
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?
Um, no. Wrong turn somewhere. It's a LOT simpler than that.
Your numerator will be :
(1-sinx)(1+sinx) - cos^2x