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treefriendly Group Title

Can someone help me prove sin^2(x)cos^2(x) = (1-cos4x)/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

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  1. hartnn Group Title
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    \(\cos 2x = 2\cos^2x-1 = 1-2\sin^2x\) so can you find cos^2x =..... ? and sin^2x =.... from this formula ?

    • one year ago
  2. treefriendly Group Title
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    Not really :/

    • one year ago
  3. hartnn Group Title
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    \(\cos 2x = 2\cos^2x-1 \) Add 1 to both sides, what u get ?

    • one year ago
  4. treefriendly Group Title
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    1 + cos2x = 2 cos^2 x?

    • one year ago
  5. hartnn Group Title
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    thats correct, now divide both sides by 2 what u get ?

    • one year ago
  6. treefriendly Group Title
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    (1+cos2x)/2 = cos^2 x?

    • one year ago
  7. hartnn Group Title
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    yes, correct. in the same way, isolate sin^2 x from \(\cos 2x = 1-2\sin^2x\)

    • one year ago
  8. treefriendly Group Title
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    so then cos2x-1 = -2sin^2 x?

    • one year ago
  9. hartnn Group Title
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    yes, now divide both sides by -2 what u get ?

    • one year ago
  10. treefriendly Group Title
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    (cos2x-1)/-2 = sin^2 x?

    • one year ago
  11. treefriendly Group Title
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    but I thought you couldn't divide by -2 because it's with the sine?

    • one year ago
  12. hartnn Group Title
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    yes, or you can say, (1-cos 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
  13. treefriendly Group Title
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    what happened to the negative sign that was on the 2?

    • one year ago
  14. hartnn Group Title
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    cos2x -1 got turned into 1-cos2x because of that negative sign.

    • one year ago
  15. treefriendly Group Title
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    ohh okay. so ((1-cos^2 x)/2) ((1+cos2x)/2)) ?

    • one year ago
  16. hartnn Group Title
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    how cos^2 x ? aren't both of them cos 2x ?

    • one year ago
  17. treefriendly Group Title
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    Darn. Yeah, you're right. I was looking at something else when I was typing

    • one year ago
  18. hartnn Group Title
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    so, ((1-cos2 x)/2) ((1+cos2x)/2)) now use \((a-b)(a+b)=a^2+b^2\) so, (1-cos2x)(1+cos2x) =... ?

    • one year ago
  19. treefriendly Group Title
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    1+cos2x-cos2x-2cos^2 x

    • one year ago
  20. hartnn Group Title
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    check your last term. its not -2cos^2x

    • one year ago
  21. treefriendly Group Title
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    errr..... -cos^2 x^2? or -cos^2 2x?

    • one year ago
  22. hartnn Group Title
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    -cos^2 2x

    • one year ago
  23. hartnn Group Title
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    so, you have 1-cos^2 2x according to \(\cos 2x = 2\cos^2x-1\) what will be cos^2 2x=... ?)

    • one year ago
  24. treefriendly Group Title
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    cos2x?

    • one year ago
  25. hartnn Group Title
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    \(\cos 2x = 2\cos^2x-1 \\cos 2(2x) = 2\cos^2(2x)-1 \\ \cos^22x =(\cos 4x+1)/2 \) got this ?

    • one year ago
  26. treefriendly Group Title
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    kind of yeah

    • one year ago
  27. hartnn Group Title
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    so, whats \(\\~ \\ 1-\cos^22x =1-(\cos 4x+1)/2=..?\)

    • one year ago
  28. treefriendly Group Title
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    cos 2 (2x) = cos ^2 (2x) ?

    • one year ago
  29. hartnn Group Title
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    ou had \( ((1-\cos2 x)/2) (1+\cos2x)/2))= (1-\cos^2 2x)/4 \\ =(2-\cos 4x-1)=1-\cos 4x\)

    • one year ago
  30. AravindG Group Title
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    @treefriendly got it now?

    • one year ago
  31. treefriendly Group Title
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    Sort of, but I'm a bit lost.

    • one year ago
  32. AravindG Group Title
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    can you tell me where?

    • one year ago
  33. treefriendly Group Title
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    The last part. What happened to the 8 from the initial equation?

    • one year ago
  34. AravindG Group Title
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    i dont see any 8 here

    • one year ago
  35. treefriendly Group Title
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    Sorry, it's getting late and I've been misreading

    • one year ago
  36. AravindG Group Title
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    i see ..then i suggest you take rest do it afresh the next day

    • one year ago
  37. treefriendly Group Title
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    I meant what happened to theta that was being divided from 1-cos4x?

    • one year ago
  38. AravindG Group Title
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    there is no theta here

    • one year ago
  39. treefriendly Group Title
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    prove sin^2(x)cos^2(x) = (1-cos4x)/theta?

    • one year ago
  40. hartnn Group Title
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    its not theta, its 8 \(((1-\cos2 x)/2) (1+\cos2x)/2))= (1-\cos^2 2x)/4 \\\\=(1-(\cos4x+1)/2)/4\\ =(2-\cos 4x-1)/8=(1-\cos 4x)/8\)

    • one year ago
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