# Can this Trig Identity be proven?

• Nov 9th 2008, 07:37 PM
casey_k
Can this Trig Identity be proven?
I couldn't solve this one:

1 + tan x/ 1 + cot x = 1 - tan x/ cot x - 1
• Nov 9th 2008, 07:40 PM
Prove It
Quote:

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).
• Nov 9th 2008, 07:41 PM
casey_k
yes.
• Nov 9th 2008, 07:45 PM
11rdc11
Yes you can prove it graphically and algebrically
• Nov 9th 2008, 07:47 PM
Prove It
Oops, edited where I should have posted...

Check my edit.
• Nov 9th 2008, 07:55 PM
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.

(Worried)
• Nov 9th 2008, 07:57 PM
Prove It
Quote:

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.

(Worried)

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.