# Proving a Trigonometric Identity

• July 22nd 2009, 09:05 PM
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.

• July 22nd 2009, 09:26 PM
skeeter
$\frac{1+\cos{a}}{1-\csc{a}} + \frac{1-\cos{a}}{1+\csc{a}}$

$\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}}
$

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

$-2\tan{a}(\tan{a}+1)$
• July 22nd 2009, 11:03 PM