Trig. Identity help please!

**sk8erboyla2004** · November 15th 2008, 06:05 PM

Im trying to study for my math 109/110 course in college
and trig. id's are giving me the hardest problems

we've learned about the identities for sin, cos, tan and excluding cot csc sec

Prove the identity

$tan x =\frac{sin 2x}{1+ cos 2x}$

also how is this and identity the x values are not the same at all I thought that what trig. identity means for every x value both have the same output

Also

how is

$\frac{cos^2t-sin^2t}{cos^2t} = 1- \frac{sin^2t}{cos^2t}$

**Math_Helper** · November 15th 2008, 06:59 PM

**sk8erboyla2004** · November 15th 2008, 07:39 PM

Um ok?
Care to explain?

**Soroban** · November 15th 2008, 09:48 PM

Hello, sk8erboyla2004!

Prove the identity: . $\tan x \:=\: \frac{\sin 2x}{1+ \cos 2x}$

You need to know some Double-angle identities:

. . $\sin 2\theta \:=\:2\sin\theta\cos\theta$

. . $\cos^2\!\theta \:=\:\frac{1 + \cos2\theta}{2} \quad\Rightarrow\quad 1 + \cos2\theta \:=\:2\cos^2\!\theta$

Then: . $\frac{\sin2x}{1+\cos2x} \;=\;\frac{2\sin x\cos x}{2\cos^2\!x} \;=\;\frac{\sin x}{\cos x} \;=\;\tan x$

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