MHB Proving a trigonometric identity

[egillesp]

Hi,

I need help proving the following trig identity:

$$\frac{\cot^2(x)-\cot(x)+1}{1-2\tan(x)+\tan^2(x)}=\frac{1+\cot^2(x)}{1+\tan^2(x)}$$

Me and my friend have spent several hours determined to figure this out, starting from the left hand side, the right hand side, and doing both together, but nothing seems to work.
For example, I tried to factor the left hand side, $$\frac{(\cot(x)-1)^2}{(\tan(x)-1)^2}$$, but it didn't get me anywhere.

Help would be greatly appreciated

 

[MarkFL]

I tried fixing your $\LaTeX$, and the resulting identity is not true...can you clarify what the actual given identity should be?

 

[egillesp]

The actual given identity is what I posted in the title and first thing in the thread

 

[MarkFL]

The actual given identity is what I posted in the title and first thing in the thread

The equation given in your first post is not an identity. :D

 

[egillesp]

okay, so what do you mean by a trig identity?

 

[MarkFL]

okay, so what do you mean by a trig identity?

An identity is an equation that is true for all legitimate values of any variables in the equation.

The equation you posted is only true for:

$$x=\frac{\pi}{2}(2k\pm1)$$ where $$k\in\mathbb{Z}$$

 

[egillesp]

okay thank you

 

[MarkFL]

okay thank you

One of the first things I do when someone posts a trigonometric identity is to use W|A to check to see if it is in fact an identity, because often enough the given identity is in fact not true, and this saves a lot of time and hair pulling. :D

Here is where I checked:

>>click here<<