Ask questions and get helpful answers.

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?
Thank you!

1. 👍
2. 👎
3. 👁
4. ℹ️
5. 🚩
3 answers
1. 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!

1. 👍
2. 👎
3. ℹ️
4. 🚩
2. 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?

1. 👍
2. 👎
3. ℹ️
4. 🚩
3. Um, no. Wrong turn somewhere. It's a LOT simpler than that.

Your numerator will be :

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

1. 👍
2. 👎
3. ℹ️
4. 🚩