Prove Trig Identity

**Raj** · November 11th 2008, 06:24 PM

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

Can't seem to prove this one, help please

**mr fantastic** · November 11th 2008, 06:58 PM

Originally Posted by Raj

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

Can't seem to prove this one, help please

Start by choosing a side.

I choose the right hand side.

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

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

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

**Raj** · November 12th 2008, 07:30 AM

Substitute

. Multiply numerator and denominator by

.

Where is the cosx coming from

**mr fantastic** · November 12th 2008, 11:52 AM

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.

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