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pottersheep

  • 2 years ago

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)

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  1. pottersheep
    • 2 years ago
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    I've been at it for so long! I cant get it :(

  2. zordoloom
    • 2 years ago
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    I can help.

  3. pottersheep
    • 2 years ago
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    Thank you so much

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

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

  6. pottersheep
    • 2 years ago
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    I think so

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

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

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

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

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

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

  13. zordoloom
    • 2 years ago
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    Okay.

  14. zordoloom
    • 2 years ago
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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.

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

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

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

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

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

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

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

  22. pottersheep
    • 2 years ago
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    yep!

  23. zordoloom
    • 2 years ago
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    good.

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

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

  26. pottersheep
    • 2 years ago
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    hmm

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

  28. pottersheep
    • 2 years ago
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    alright

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

  30. pottersheep
    • 2 years ago
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    yep

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

  32. pottersheep
    • 2 years ago
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    yep

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

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

  35. zordoloom
    • 2 years ago
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    yes.

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

  37. pottersheep
    • 2 years ago
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    sorry ><

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

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

  40. pottersheep
    • 2 years ago
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    Of course

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

  42. pottersheep
    • 2 years ago
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    :D

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

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

  46. zordoloom
    • 2 years ago
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    Yep.

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