# Thread: Can this Trig Identity be proven?

1. ## Can this Trig Identity be proven?

I couldn't solve this one:

1 + tan x/ 1 + cot x = 1 - tan x/ cot x - 1

2. Originally Posted by casey_k
I couldn't solve this one:

1 + tan x/ 1 + cot x = 1 - tan x/ cot x - 1
Is that $\displaystyle \frac{1+\tan{x}}{1+\cot{x}} = \frac{1 - \tan{x}}{\cot{x} - 1}$? Please put brackets where they're required...

Turn the cots into tans. You should be able to show that both sides equal tan(x).

yes.

4. Yes you can prove it graphically and algebrically

5. Oops, edited where I should have posted...

Check my edit.

6. ## ?

how do i prove it algebraically?

I tried to prove it and got tan but not $\displaystyle \frac{1 - \tan{x}}{\cot{x} - 1}$ when i used the left side.

7. Originally Posted by casey_k
how do i prove it algebraically?

I tried to prove it and got tan but not $\displaystyle \frac{1 - \tan{x}}{\cot{x} - 1}$ when i used the left side.

You've gotten the left hand side to equal tan.

If you can show that the right hand side also equals tan, then obviously they're equal.