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treefriendly
 2 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
 2 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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

hartnn
 2 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
 2 years ago
Best ResponseYou've already chosen the best response.0@treefriendly got it now?

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

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

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

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

AravindG
 2 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
 2 years ago
Best ResponseYou've already chosen the best response.0I meant what happened to theta that was being divided from 1cos4x?

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

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

hartnn
 2 years ago
Best ResponseYou've already chosen the best response.0its not theta, its 8 \(((1\cos2 x)/2) (1+\cos2x)/2))= (1\cos^2 2x)/4 \\\\=(1(\cos4x+1)/2)/4\\ =(2\cos 4x1)/8=(1\cos 4x)/8\)
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