# Thread: Using algebra to prove an identity

1. ## Using algebra to prove an identity

Use algebra to prove the identity.

I can't seem to get a 1 on the numerator of the left equation. Here is what I got:

(cosx/1-sin x) - tan x = 1/cos x
(cosx/1-sin x) - sinx/cosx = 1/cos x
(Minus both equations so it looks something like this)
((cosx)(cosx) - sin(1-sin t))/((1-sinx)(cosx))

After the last stage no matter what I do I cannot get just a 1 on the numerator of the left equation. I have tried multiplying out the (cosx)(cosx) to become cos^2x and turning that into -sin^2x + 1 but still I would have a sin left on the top. Please help me with this. Thank you very much!

2. Originally Posted by florx

Use algebra to prove the identity.

I can't seem to get a 1 on the numerator of the left equation. Here is what I got:

(cosx/1-sin x) - tan x = 1/cos x
(cosx/1-sin x) - sinx/cosx = 1/cos x
(Minus both equations so it looks something like this)
((cosx)(cosx) - sin(1-sin t))/((1-sinx)(cosx))

After the last stage no matter what I do I cannot get just a 1 on the numerator of the left equation. I have tried multiplying out the (cosx)(cosx) to become cos^2x and turning that into -sin^2x + 1 but still I would have a sin left on the top. Please help me with this. Thank you very much!
The fourth line of the attempt you made should look like this:

$\displaystyle \frac{cosx(cosx) - sinx(1-sinx)}{cosx(1-sinx)}$

$\displaystyle = \frac{cos^2x - sinx +sin^2x}{cosx(1-sinx)}$

try taking it further now!

3. Wow I used to just cancel out the (1 - sinx) right there and then so that is why I never got the correct answer. Thank you so much for your persistence in helping me!