$$dfrac2sin (x)cos(x)1-2cos(x)-1 = dfrac2sin(x)cos(x)-2cos^2(x) = dfrac2sin(x)-2cos(x) = - an (x)$$

I think I"ve gone wrong somewhere.

You are watching: Simplify cos^2x-sin^2x

We have

$$cos(2x) = cos^2x-sin^2x=2cos^colorred2(x)-1=1-2sin^2 x$$

and then

$$dfracsin(2x)1-cos (2x)=dfrac2sin x cos x1-1+2sin^2 x=cot x$$

You gained one the the indications mixed up.

$$fracsin(2x)1-cos (2x) = dfracsin(2x)1-(2cos^2x-1) = fracsin(2x)1-2cos^2x+1$$

Instead, girlfriend accidentally used

$$fracsin(2x)1-cos (2x) colorred eq fracsin(2x)1-2cos^2x-1$$

As for the leveling itself,

$$fracsin(2x)1-cos (2x) = frac2sin xcos x1-(1-2sin^2x) = frac2sin xcos x2sin^2 x = fraccos xsin x = cot x$$

Also, to allude out, you offered $cos(2x) = 2cos^2x-1$, which no actually acquire you anywhere since you acquire two $+1$’s. Using $cos^2x = 1-2sin^2x$ is the way to go.

re-superstructure

mention

follow

edited Nov 23 "18 in ~ 20:45

reply Nov 23 "18 in ~ 20:40

KM101KM101

7,07611 gold badge88 silver- badges2626 bronze title

$endgroup$

include a comment |

2

$egingroup$

$$frac2sin xcos x1-(1-2sin^2x)=fraccos xsin x.$$

re-publishing

cite

monitor

edited Nov 23 "18 in ~ 21:05

answer Nov 23 "18 in ~ 20:50

user65203user65203

$endgroup$

add a comment |

## her Answer

Thanks because that contributing response to katifund.org Stack Exchange!

Please be sure to*answer the question*. Provide details and share your research!

But *avoid* …

Use katifund.orgJax to style equations. katifund.orgJax reference.

To learn more, see our advice on writing great answers.

See more: Gallery: Super Mario Party Logo, Free Transparent Mario Party Logo Images, Page 1

Draft saved

Draft discarded

### Sign increase or log in

sign up utilizing Google

sign up using Facebook

authorize up making use of Email and also Password

send

### Post together a guest

surname

email Required, yet never shown

### Post as a guest

name

Required, however never shown

short article Your answer Discard

By clicking “Post her Answer”, friend agree to our terms of service, privacy policy and cookie plan

## Not the price you're looking for? Browse other questions tagged trigonometry or questioning your own question.

The Overflow Blog

Featured ~ above Meta

related

1

just how do i simplify $cos(4x)cos(3x)−4sin(x)sin(3x)cos(x)cos(2x)$?

3

Proving that $fracsin alpha + sin etacos alpha + cos eta = an left ( fracalpha+eta2 ight )$

1

simplify $fraccos(2x)cot(x)-1-fracsin(2x)2$

1

exactly how does $int_pi/3^pi/2 frac1-cos^2xsqrtsin^2(x/2)dx$ leveling to $int_pi/3^pi/2 4sin(x/2)cos^2(x/2)dx$?

2

prove $fracsin 2x - cos x4sin^2x -1 = fracsin^2x+cos x+cos^2x2sin x +1 $

3

Verify the identity $frac an(a+b) an(a-b)$ = $fracsin(a)cos(a)+sin(b)cos(b)sin(a)cos(a)-sin(b)cos(b)$

1

exactly how do I leveling $4sin(2a) - 2sin(2a) cdot 4sin^2(a)$?

3

proving $fraccos A - cos Bsin A + sin B = fracsin B - sin Acos A + cos B$

hot Network concerns more hot concerns

inquiry feed

subscribe to RSS

inquiry feed To i ordered it to this RSS feed, copy and paste this URL right into your RSS reader.

katifund.orgematics

agency

stack Exchange Network

site style / logo design © 2021 stack Exchange Inc; user contributions licensed under cc by-sa. Rev2021.10.28.40586

katifund.orgematics ridge Exchange works best with JavaScript enabled

her privacy

By clicking “Accept every cookies”, friend agree stack Exchange deserve to store cookies on your machine and disclose info in accordance v our Cookie Policy.