# Math Help - Proving a Trigonometric Identity

1. ## Proving a Trigonometric Identity

I'm not sure how I should go about answering this question as I need to find how the LHS becomes the RHS. I've done a bit of working but I'm not sure if it's correct and if it is I'm not sure where to go from there. (See attachments) If someone could show me how to work through the problem like I have, it would be greatly appreciated.

2. $\frac{1+\cos{a}}{1-\csc{a}} + \frac{1-\cos{a}}{1+\csc{a}}$

$\frac{(1+\cos{a})(1+\csc{a}) + (1-\cos{a})(1-\csc{a})}{1-\csc^2{a}}
$

$\frac{1+\csc{a}+\cos{a}+\cot{a} + 1 -\csc{a}-\cos{a}+\cot{a}}{-\cot^2{a}}$

$\frac{2 + 2\cot{a}}{-\cot^2{a}}
$

$-2\tan^2{a} - 2\tan{a}$

$-2\tan{a}(\tan{a}+1)$

3. Thanks skeeter,

I was really close to getting that, I didn't think about changing cosA/sinA to cotA, this really helped a lot.