# Thread: Trigonometric Identy problem problem

1. ## Trigonometric Identy problem problem

cos x - 1
----------
sin x

+

sin x
-------------
cos x + 1

I have been working on this for a while now and have yet to come up with a way to get the correct answer. I know that the answer is 0 but I have no idea how to do it correctly any help is greatly appriciated

2. Originally Posted by aeswork
cos x - 1
----------
sin x

+

sin x
-------------
cos x + 1

I have been working on this for a while now and have yet to come up with a way to get the correct answer. I know that the answer is 0 but I have no idea how to do it correctly any help is greatly appriciated

$\displaystyle \frac{\cos{x}-1}{\sin{x}} + \frac{\sin{x}}{\cos{x}+1}$

get a common denominator and add the fractions ...

$\displaystyle \frac{(\cos{x}-1)(\cos{x}+1)}{\sin{x}(\cos{x}+1)} + \frac{\sin^2{x}}{\sin{x}(\cos{x}+1)}$

$\displaystyle \frac{\cos^2{x} - 1 + \sin^2{x}}{\sin{x}(\cos{x}+1)}$

finish it

3. thank you so much, its things like that, that I just don't see that make math so amazing and fun to learn.

4. If this is a proof, what is it equal to? Have you tried to make a common denominator?

5. Originally Posted by pickslides
If this is a proof, what is it equal to? Have you tried to make a common denominator?
It's equal to zero because sin^2(x)+cos^2(x)=1. and that's what aeswork wanted to be proved!