Asked by Momo

Solve this equation algebraically:

(1-sin x)/cos x = cos x/(1+sin x)

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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!
Answered by 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

(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!
Answered by 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?
Answered by jim
Um, no. Wrong turn somewhere. It's a LOT simpler than that.

Your numerator will be :

(1-sinx)(1+sinx) - cos^2x



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