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sabika13

how do prove this identity: sin^4x -cos^4x=1-2cos^2x

  • one year ago
  • one year ago

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  1. zordoloom
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    Do you still need help?

    • one year ago
  2. sabika13
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    RS: (sin^2x+cos^2x)-2cos^2x sin^2x-cos^2x Thats how much i can simplify right side..

    • one year ago
  3. sabika13
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    yah

    • one year ago
  4. zordoloom
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    alright.

    • one year ago
  5. zordoloom
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    So here is how I proved it:

    • one year ago
  6. zordoloom
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    So, change sinx^4 to (1-cosx^2)^2

    • one year ago
  7. zordoloom
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    You can expand that and you get 1-2cosx^2+cosx^4-cosx^4=1-2cosx^2

    • one year ago
  8. zordoloom
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    Do you follow so far?

    • one year ago
  9. zordoloom
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    @sabika13 Should I continue?

    • one year ago
  10. sabika13
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    yes sorry

    • one year ago
  11. zordoloom
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    ok

    • one year ago
  12. zordoloom
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    When you simplify 1-2cosx^2+cosx^4-cosx^4=1-2cosx^2, the left side becomes 1-2cosx^2=1-2cosx^2

    • one year ago
  13. zordoloom
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    That proves the identity.

    • one year ago
  14. zordoloom
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    Normally, when you prove an identity, you work on one side. In this problem I worked on the left side.

    • one year ago
  15. sabika13
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    wait how does (1-2cosx^2)^2=1-2cos^2+cosx^4?

    • one year ago
  16. zordoloom
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    To summarize it: You have sin(x)^4-cos(x)^4=1-2cos(x)^2 change sin(x)^4 --->(1-cos(x)^2)^2 You have: (1-cos(x)^2)^2-cos(x)^4=1-2cos(x)^2 Then expand (1-cos(x)^2)^2 on the left side. You get 1-2cos(x)^2+cos(x)^4-cos(x)^4=1-2cos(x)^2

    • one year ago
  17. zordoloom
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    Any better?

    • one year ago
  18. zordoloom
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    Then the: cos(x)^4-cos(x)^4 cancel out.

    • one year ago
  19. zordoloom
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    Hope that helped.

    • one year ago
  20. sabika13
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    im having problems expanding (1-cos^2x)^2 shouldnt it be: 1-cos^4x :S

    • one year ago
  21. zordoloom
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    So, (1-cos^2x)(1-cos^2x). Just foil out.

    • one year ago
  22. sabika13
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    ohhh okay, but why is it not: (1-cos^2x)(1+cos^2x)

    • one year ago
  23. zordoloom
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    It's squared. It's not a difference of squares.

    • one year ago
  24. sabika13
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    ohh i think i get it...

    • one year ago
  25. zordoloom
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    Any number, or equation squared is the same as it times by itself. Example (6)^2= (6)*(6) or (3x-2)^2= (3x-2)(3x-2). Do you get the point?

    • one year ago
  26. zordoloom
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    You don't change the signs inside the equation.

    • one year ago
  27. sabika13
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    yeah so whats difference of squares then (if you dont mind me asking)

    • one year ago
  28. zordoloom
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    example x^2-4. When you factor it, you get (x-2)(x+2). It's a^2-b^2

    • one year ago
  29. sabika13
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    ohhh thankkyou!!you helped me fix a very big misconception inmy head ;P

    • one year ago
  30. zordoloom
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    yep, no prob.

    • one year ago
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