# Thread: Prove this is an Identity

1. ## Prove this is an Identity

I am having trouble with this problem;
$\frac {tanx}{1-cotx}+\frac{cotx}{1-tanx}=1+secxcscx$

I have tired multiplying each fraction by the other denominator and have got stuck. I then tried to multiple each fraction by the its conjugate to get the identity but then I get stuck that way also. Then I tried the right side and got a common denominator then didn't know where to go form there.

Thanks for the help. Its greatly appreciated.

2. $\displaystyle \frac{t}{1-1/t}+\frac{1/t}{1-t} = \frac{t^2}{t-1}+\frac{1}{t(1-t)} = \frac{t^3-1}{t(t-1)} = \frac{t^2+t+1}{t} = 1+t+\frac{1}{t}$

Therefore your LHS is equivalent to $1+\tan{x}+\cot{x}$. So all that's left is to show that:

................................... $\tan{x}+\cot{x} = \sec{x}\csc{x}$.