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pottersheep Group Title

I really need help with this Trig identity please!(Grade 12!) How do I prove that sinx-siny = 2cos([x+y]/2)sin([x+y]/2)

  • 2 years ago
  • 2 years ago

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  1. pottersheep Group Title
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    I've been at it for so long! I cant get it :(

    • 2 years ago
  2. zordoloom Group Title
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    I can help.

    • 2 years ago
  3. pottersheep Group Title
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    Thank you so much

    • 2 years ago
  4. pottersheep Group Title
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    We have only learnt compound angles, by the way

    • 2 years ago
  5. zordoloom Group Title
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    So there is an identity that's called co function identies, do you know them?

    • 2 years ago
  6. pottersheep Group Title
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    I think so

    • 2 years ago
  7. zordoloom Group Title
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    Or sum to product identities. Do any of these sound familiar.

    • 2 years ago
  8. pottersheep Group Title
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    Is it the cos(90-x) kind of thing?

    • 2 years ago
  9. zordoloom Group Title
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    um, not really. Here, let me post a link.

    • 2 years ago
  10. zordoloom Group Title
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    http://www.sosmath.com/trig/Trig5/trig5/trig5.html

    • 2 years ago
  11. pottersheep Group Title
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    Thanks Ill read it!

    • 2 years ago
  12. pottersheep Group Title
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    nope....never learnt those :s

    • 2 years ago
  13. zordoloom Group Title
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    Okay.

    • 2 years ago
  14. zordoloom Group Title
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    Give me like 5-10 minutes. This one is a little tricky. I'll try to keep you updated with the steps.

    • 2 years ago
  15. pottersheep Group Title
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    Alright I really appreciate it

    • 2 years ago
  16. pottersheep Group Title
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    I found a note that our teacher wrote on the board! I dont get it though... he wrote

    • 2 years ago
  17. pottersheep Group Title
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    sinx + siny = sin(a+b) = sinacosB + cosAsinB sin(a-b) = sinAcosB - cosAsinB sin(a+B) + sin (a - b) = 2sinAcosB

    • 2 years ago
  18. pottersheep Group Title
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    ignore the caps they are the same letter

    • 2 years ago
  19. pottersheep Group Title
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    Then he wrote : let : a+b = x a - b = y 2a = x+y x = (x+y)/2

    • 2 years ago
  20. zordoloom Group Title
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    still working....

    • 2 years ago
  21. zordoloom Group Title
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    Okay, Do you know the double angle formula?

    • 2 years ago
  22. pottersheep Group Title
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    yep!

    • 2 years ago
  23. zordoloom Group Title
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    good.

    • 2 years ago
  24. zordoloom Group Title
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    okay, so cos([x+y]/2)sin([x+y]/2). This equal sin(x+y)

    • 2 years ago
  25. zordoloom Group Title
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    Are you following what i mean here?

    • 2 years ago
  26. pottersheep Group Title
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    hmm

    • 2 years ago
  27. zordoloom Group Title
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    how about this. 2cosAsinA=sin2a. A=(x+y)/2

    • 2 years ago
  28. pottersheep Group Title
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    alright

    • 2 years ago
  29. zordoloom Group Title
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    cosine of x is sine of (90-x) right?

    • 2 years ago
  30. pottersheep Group Title
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    yep

    • 2 years ago
  31. zordoloom Group Title
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    okay. so =sin(x+y) =sinxcosy+sinycosx =sinx sin(90-y)+siny sin(90-x)

    • 2 years ago
  32. pottersheep Group Title
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    yep

    • 2 years ago
  33. zordoloom Group Title
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    I have a quick question, is it sin(x+y)/2 or sin(x-y)/2?

    • 2 years ago
  34. pottersheep Group Title
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    one sec for the original question?

    • 2 years ago
  35. zordoloom Group Title
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    yes.

    • 2 years ago
  36. pottersheep Group Title
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    oh no! you are right it sin(x-y)!!!!!!!

    • 2 years ago
  37. pottersheep Group Title
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    sorry ><

    • 2 years ago
  38. zordoloom Group Title
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    Ok, that makes more sense now.

    • 2 years ago
  39. zordoloom Group Title
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    Give me another minute to type this up.

    • 2 years ago
  40. pottersheep Group Title
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    Of course

    • 2 years ago
  41. zordoloom Group Title
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    ok, i've got it.

    • 2 years ago
  42. pottersheep Group Title
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    :D

    • 2 years ago
  43. zordoloom Group Title
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    • 2 years ago
  44. zordoloom Group Title
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    ok let me know if you can see it.

    • 2 years ago
  45. pottersheep Group Title
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    I can see it! Im following through fine so far. Thank you so much

    • 2 years ago
  46. zordoloom Group Title
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    Yep.

    • 2 years ago
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