A community for students.
Here's the question you clicked on:
 0 viewing
treefriendly
 3 years 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
treefriendly
 3 years 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

This Question is Open

hartnn
 3 years ago
Best 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 ?

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

treefriendly
 3 years ago
Best ResponseYou've already chosen the best response.01 + cos2x = 2 cos^2 x?

hartnn
 3 years ago
Best ResponseYou've already chosen the best response.0thats correct, now divide both sides by 2 what u get ?

treefriendly
 3 years ago
Best ResponseYou've already chosen the best response.0(1+cos2x)/2 = cos^2 x?

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

treefriendly
 3 years ago
Best ResponseYou've already chosen the best response.0so then cos2x1 = 2sin^2 x?

hartnn
 3 years ago
Best ResponseYou've already chosen the best response.0yes, now divide both sides by 2 what u get ?

treefriendly
 3 years ago
Best ResponseYou've already chosen the best response.0(cos2x1)/2 = sin^2 x?

treefriendly
 3 years ago
Best ResponseYou've already chosen the best response.0but I thought you couldn't divide by 2 because it's with the sine?

hartnn
 3 years ago
Best ResponseYou've already chosen the best response.0yes, 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 =... ?

treefriendly
 3 years ago
Best ResponseYou've already chosen the best response.0what happened to the negative sign that was on the 2?

hartnn
 3 years ago
Best ResponseYou've already chosen the best response.0cos2x 1 got turned into 1cos2x because of that negative sign.

treefriendly
 3 years ago
Best ResponseYou've already chosen the best response.0ohh okay. so ((1cos^2 x)/2) ((1+cos2x)/2)) ?

hartnn
 3 years ago
Best ResponseYou've already chosen the best response.0how cos^2 x ? aren't both of them cos 2x ?

treefriendly
 3 years ago
Best ResponseYou've already chosen the best response.0Darn. Yeah, you're right. I was looking at something else when I was typing

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

treefriendly
 3 years ago
Best ResponseYou've already chosen the best response.01+cos2xcos2x2cos^2 x

hartnn
 3 years ago
Best ResponseYou've already chosen the best response.0check your last term. its not 2cos^2x

treefriendly
 3 years ago
Best ResponseYou've already chosen the best response.0errr..... cos^2 x^2? or cos^2 2x?

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

hartnn
 3 years ago
Best 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 ?

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

treefriendly
 3 years ago
Best ResponseYou've already chosen the best response.0cos 2 (2x) = cos ^2 (2x) ?

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

AravindG
 3 years ago
Best ResponseYou've already chosen the best response.0@treefriendly got it now?

treefriendly
 3 years ago
Best ResponseYou've already chosen the best response.0Sort of, but I'm a bit lost.

AravindG
 3 years ago
Best ResponseYou've already chosen the best response.0can you tell me where?

treefriendly
 3 years ago
Best ResponseYou've already chosen the best response.0The last part. What happened to the 8 from the initial equation?

treefriendly
 3 years ago
Best ResponseYou've already chosen the best response.0Sorry, it's getting late and I've been misreading

AravindG
 3 years ago
Best ResponseYou've already chosen the best response.0i see ..then i suggest you take rest do it afresh the next day

treefriendly
 3 years ago
Best ResponseYou've already chosen the best response.0I meant what happened to theta that was being divided from 1cos4x?

AravindG
 3 years ago
Best ResponseYou've already chosen the best response.0there is no theta here

treefriendly
 3 years ago
Best ResponseYou've already chosen the best response.0prove sin^2(x)cos^2(x) = (1cos4x)/theta?

hartnn
 3 years ago
Best ResponseYou've already chosen the best response.0its not theta, its 8 \(((1\cos2 x)/2) (1+\cos2x)/2))= (1\cos^2 2x)/4 \\\\=(1(\cos4x+1)/2)/4\\ =(2\cos 4x1)/8=(1\cos 4x)/8\)
Ask your own question
Sign UpFind more explanations on OpenStudy
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.