• November 15th 2008, 07:05 PM
sk8erboyla2004
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

$\frac{cos^2t-sin^2t}{cos^2t} = 1- \frac{sin^2t}{cos^2t}$
• November 15th 2008, 07:59 PM
Math_Helper
• November 15th 2008, 08:39 PM
sk8erboyla2004
Um ok?
Care to explain?
• November 15th 2008, 10:48 PM
Soroban
Hello, sk8erboyla2004!

Quote:

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