# Thread: Hint to proof this identity

1. ## Hint to proof this identity

Hi,

Can anyone give me a hint/tip to get started with this question. I've been at it for an hour and just get a mish mash of sin and cos:

Prove:

$\displaystyle \frac{cos(A)}{1 - tan(A)} + \frac{sin(A)}{1-cot(A)} = sin(A) + sin(A)$

Thank you

2. Originally Posted by aceband
Hi,

Can anyone give me a hint/tip to get started with this question. I've been at it for an hour and just get a mish mash of sin and cos:

Prove:

$\displaystyle \frac{cos(A)}{1 - tan(A)} + \frac{sin(A)}{1-cot(A)} = sin(A) + sin(A)$

Thank you
correction
you mean you want to prove this right ??

$\displaystyle \frac{cos(A)}{1 - tan(A)} + \frac{sin(A)}{1-cot(A)} = cos(A) + sin(A)$

to prove it first you know that

$\displaystyle \tan A = \frac{\sin A }{\cos A }$

$\displaystyle \cot A = \frac{\cos A}{\sin A }$

$\displaystyle 1- \frac{\sin A }{\cos A } = \frac{\cos A - \sin A }{\cos A }$

make the same thing to the other denominator
simplify you will have to fraction have the same denominator
use
$\displaystyle (a^2 - b^2 ) = (a-b)(a+b)$

something will cancel then you will get the answer

3. Thank you!!

Also a million thanks Sorban, i can't thank you in a private message yet because my post count isn't high enough so i'm doing it here