# Help with trig identities

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• Apr 6th 2008, 08:40 PM
kelsey3
Help with trig identities
verify the identity: tanxcos(squared)x=[(2tanxcos(squared)x-tanx)/(1-tan(squared)x]
• Apr 6th 2008, 08:46 PM
Mathstud28
Wow your trig teacher is sadistic
$\frac{sin(x)}{cos(x)}\cdot[cos(x)^2]=\frac{\frac{2sin(x)}{cos(x)^3}-\frac{sin(x)}{cos(x)}}{sec(x)^2-2}$..can you see whta to do from there
• Apr 6th 2008, 08:49 PM
Jhevon
Quote:

Originally Posted by kelsey3
verify the identity: tanxcos(squared)x=[(2tanxcos(squared)x-tanx)/(1-tan(squared)x]

with identities, always start with the more complicated side (the right side in this case). change everything to sine and cosines and then simplify

recommendations here: factor out the tangent first. remember your identities for cos(2x)
• Apr 6th 2008, 08:50 PM
Jhevon
Quote:

Originally Posted by Mathstud28
$\frac{sin(x)}{cos(x)}\cdot[cos(x)^2]=\frac{\frac{2sin(x)}{cos(x)^3}-\frac{sin(x)}{cos(x)}}{sec(x)^2-2}$..can you see whta to do from there

it's actually not that bad a problem if you factor out tangent first...
• Apr 6th 2008, 08:51 PM
Mathstud28
Haha
I think your secondary purpose on here is to help people with math...I think your primary purpose is to point out a highschooler(me)'s flaws..haha just kidding
• Apr 6th 2008, 08:55 PM
Jhevon
Quote:

Originally Posted by Mathstud28
I think your secondary purpose on here is to help people with math...I think your primary purpose is to point out a highschooler(me)'s flaws..haha just kidding

hehe, i was thinking the same thing, haha. it seems i have been picking on you a lot tonight, huh?

don't worry about it, when i just started here, the same thing happened to me. just look through some of my old posts, i was constantly making a fool of myself (i still do sometimes).

it's tough love. i have nothing against you. trust me, it will help you in the long run. if you feel like someone's always there to critique you, you'll start to think things through more carefully.

Power to you!
• Apr 6th 2008, 08:58 PM
kelsey3
ya no kiddin....i dont really get how you got the sec(squared)x-2 on the bottom and where the cos(squared)x went. I don't know what identity you used.
• Apr 6th 2008, 09:03 PM
Mathstud28
Here you go
$sec(x)^2=tan(x)^2+1$ and I made a little error...dont worry I know what I am doing the cos(x)^2 went to the bottom
• Apr 6th 2008, 09:13 PM
kelsey3
man im retarded......i got (sinx/cosx)/(1/cos(squared)x-2) and then i brought the bottom up and crossed out a cosine but its still not right
• Apr 6th 2008, 09:16 PM
Mathstud28
I am sorry
what exactly does that mean..show me your steps and I will critque you...use LaTeX if you can
• Apr 6th 2008, 09:18 PM
kelsey3
how do i use that?....im new at this...
• Apr 6th 2008, 09:19 PM
kelsey3
i just don't know how to get rid of the 2 on the bottom
• Apr 6th 2008, 09:22 PM
Mathstud28
To write it do this
the most important thing you will need to know is the fraction $\frac{cos(x)}{sin(x)}=cot(x)$ is made by[ math]\frac{cos(x)}{sin(x)}=cot(x)[/math but i took off the ] after /math...look up LaTeX if you plan on using this site often it is a neccessity to learn
• Apr 6th 2008, 09:24 PM
kelsey3
Dude.....that looks way too complicated. I just dont know how to get rid of the 2 on the bottom....i get the rest
• Apr 6th 2008, 09:25 PM
Jhevon
Quote:

Originally Posted by kelsey3
how do i use that?....im new at this...

see the tutorial here for how to use LaTeX

i will start you off.

Consider the RHS:

$\displaystyle \frac {2 \tan x \cos^2 x - \tan x}{1 - \tan^2 x} = \tan x \cdot \frac {2 \cos^2 x - 1}{1 - \frac {\sin^2 x}{\cos^2 x}}$

$\displaystyle = \tan x \cdot \frac {2 \cos^2 x - 1}{\frac {\cos^2 x - \sin^2 x}{\cos^2 x}}$

$= \frac {\sin x}{\cos x} \cdot {\color{red}2 \cos^2 x - 1} \cdot \frac {\cos^2 x}{{\color{red}\cos^2 x - \sin^2 x}}$

now what? (of course, i put the two things in red for a reason)
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