1. ## Prove Trig Identity

$\displaystyle \frac{cos2x}{sin2x+1} = \frac{1-tanx}{1+tanx}$

Can't seem to prove this one, help please

2. Originally Posted by Raj
$\displaystyle \frac{cos2x}{sin2x+1} = \frac{1-tanx}{1+tanx}$

Can't seem to prove this one, help please
Start by choosing a side.

I choose the right hand side.

Substitute $\displaystyle \tan x = \frac{\sin x}{\cos x}$. Multiply numerator and denominator by $\displaystyle \cos x$.

Now multiply numerator and denominator by $\displaystyle \cos x + \sin x$ and expand.

You should recognise the numerator as $\displaystyle \cos (2x)$. Simplify the denominator to recognise $\displaystyle \sin (2x)$.

3. Substitute . Multiply numerator and denominator by .
Where is the cosx coming from

4. Originally Posted by Raj
Where is the cosx coming from
Did you do the substitution?

If you did it should be perfectly clear where the cos x comes from. You multiply top and bottom by cos x to get rid of the fraction.

You have to actually do each of the suggested steps before you'll see why you do them.