Got Homework?
Connect with other students for help. It's a free community.
Here's the question you clicked on:
 0 viewing
Can someone help me prove sin^2(x)cos^2(x) = (1cos4x)/theta?
I'm having trouble with trigonometry and I can't really grasp the material. Please and thank you
 one year ago
 one year ago
Can someone help me prove sin^2(x)cos^2(x) = (1cos4x)/theta? I'm having trouble with trigonometry and I can't really grasp the material. Please and thank you
 one year ago
 one year ago

This Question is Open

hartnnBest ResponseYou've already chosen the best response.0
\(\cos 2x = 2\cos^2x1 = 12\sin^2x\) so can you find cos^2x =..... ? and sin^2x =.... from this formula ?
 one year ago

hartnnBest ResponseYou've already chosen the best response.0
\(\cos 2x = 2\cos^2x1 \) Add 1 to both sides, what u get ?
 one year ago

treefriendlyBest ResponseYou've already chosen the best response.0
1 + cos2x = 2 cos^2 x?
 one year ago

hartnnBest ResponseYou've already chosen the best response.0
thats correct, now divide both sides by 2 what u get ?
 one year ago

treefriendlyBest ResponseYou've already chosen the best response.0
(1+cos2x)/2 = cos^2 x?
 one year ago

hartnnBest ResponseYou've already chosen the best response.0
yes, correct. in the same way, isolate sin^2 x from \(\cos 2x = 12\sin^2x\)
 one year ago

treefriendlyBest ResponseYou've already chosen the best response.0
so then cos2x1 = 2sin^2 x?
 one year ago

hartnnBest ResponseYou've already chosen the best response.0
yes, now divide both sides by 2 what u get ?
 one year ago

treefriendlyBest ResponseYou've already chosen the best response.0
(cos2x1)/2 = sin^2 x?
 one year ago

treefriendlyBest ResponseYou've already chosen the best response.0
but I thought you couldn't divide by 2 because it's with the sine?
 one year ago

hartnnBest ResponseYou've already chosen the best response.0
yes, or you can say, (1cos 2x)/2 = sin^2 x you can divide, there's no problem with that. now substitute both these results in left side of your equation sin^2x . cos^2x =... ?
 one year ago

treefriendlyBest ResponseYou've already chosen the best response.0
what happened to the negative sign that was on the 2?
 one year ago

hartnnBest ResponseYou've already chosen the best response.0
cos2x 1 got turned into 1cos2x because of that negative sign.
 one year ago

treefriendlyBest ResponseYou've already chosen the best response.0
ohh okay. so ((1cos^2 x)/2) ((1+cos2x)/2)) ?
 one year ago

hartnnBest ResponseYou've already chosen the best response.0
how cos^2 x ? aren't both of them cos 2x ?
 one year ago

treefriendlyBest ResponseYou've already chosen the best response.0
Darn. Yeah, you're right. I was looking at something else when I was typing
 one year ago

hartnnBest ResponseYou've already chosen the best response.0
so, ((1cos2 x)/2) ((1+cos2x)/2)) now use \((ab)(a+b)=a^2+b^2\) so, (1cos2x)(1+cos2x) =... ?
 one year ago

treefriendlyBest ResponseYou've already chosen the best response.0
1+cos2xcos2x2cos^2 x
 one year ago

hartnnBest ResponseYou've already chosen the best response.0
check your last term. its not 2cos^2x
 one year ago

treefriendlyBest ResponseYou've already chosen the best response.0
errr..... cos^2 x^2? or cos^2 2x?
 one year ago

hartnnBest ResponseYou've already chosen the best response.0
so, you have 1cos^2 2x according to \(\cos 2x = 2\cos^2x1\) what will be cos^2 2x=... ?)
 one year ago

hartnnBest ResponseYou've already chosen the best response.0
\(\cos 2x = 2\cos^2x1 \\cos 2(2x) = 2\cos^2(2x)1 \\ \cos^22x =(\cos 4x+1)/2 \) got this ?
 one year ago

hartnnBest ResponseYou've already chosen the best response.0
so, whats \(\\~ \\ 1\cos^22x =1(\cos 4x+1)/2=..?\)
 one year ago

treefriendlyBest ResponseYou've already chosen the best response.0
cos 2 (2x) = cos ^2 (2x) ?
 one year ago

hartnnBest ResponseYou've already chosen the best response.0
ou had \( ((1\cos2 x)/2) (1+\cos2x)/2))= (1\cos^2 2x)/4 \\ =(2\cos 4x1)=1\cos 4x\)
 one year ago

AravindGBest ResponseYou've already chosen the best response.0
@treefriendly got it now?
 one year ago

treefriendlyBest ResponseYou've already chosen the best response.0
Sort of, but I'm a bit lost.
 one year ago

AravindGBest ResponseYou've already chosen the best response.0
can you tell me where?
 one year ago

treefriendlyBest ResponseYou've already chosen the best response.0
The last part. What happened to the 8 from the initial equation?
 one year ago

AravindGBest ResponseYou've already chosen the best response.0
i dont see any 8 here
 one year ago

treefriendlyBest ResponseYou've already chosen the best response.0
Sorry, it's getting late and I've been misreading
 one year ago

AravindGBest ResponseYou've already chosen the best response.0
i see ..then i suggest you take rest do it afresh the next day
 one year ago

treefriendlyBest ResponseYou've already chosen the best response.0
I meant what happened to theta that was being divided from 1cos4x?
 one year ago

AravindGBest ResponseYou've already chosen the best response.0
there is no theta here
 one year ago

treefriendlyBest ResponseYou've already chosen the best response.0
prove sin^2(x)cos^2(x) = (1cos4x)/theta?
 one year ago

hartnnBest ResponseYou've already chosen the best response.0
its not theta, its 8 \(((1\cos2 x)/2) (1+\cos2x)/2))= (1\cos^2 2x)/4 \\\\=(1(\cos4x+1)/2)/4\\ =(2\cos 4x1)/8=(1\cos 4x)/8\)
 one year ago
See more questions >>>
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.