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Thread: prove sin3x=(sinx)(3-4sin^2x), solve sin3x=0, prove csc(x-y)

  1. #1

    prove sin3x=(sinx)(3-4sin^2x), solve sin3x=0, prove csc(x-y)

    i have a couple of problem here that have been giving me trouble if you can solve any of them that would be great!!

    Prove
    1. sin3x=(sinx)(3-4sin^2x)

    solve for all values in the interval (0-2pie)
    2. sin3x=0

    Prove
    3. csc(x-y)= sec y/ sinx-cosx tany

  2. #2
    Senior Member
    Join Date
    Aug 2007
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    1,303

    Re: it stumped me

    1. sin3x=(sinx)(3-4sin^2x)

    Start by changing sin3x to sin(2x+x) then use the addition/subtraction identities and go from there. It worked out for me.

  3. #3

    Re: it stumped me

    yes i did that and then i did one more step but after that i just am getting really confused

  4. #4

    Re: it stumped me

    does anyone have any answers i really need them today. thanks so much

  5. #5
    Senior Member
    Join Date
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    Re: prove sin3x=(sinx)(3-4sin^2x), solve sin3x=0, prove csc(x-y)

    sin3x=(sinx)(3-4sin^2x)

    sin3x=
    sin(2x+x)=
    sin2x cosx + cos2x sinx =

    Eliminate the "2x"s by using identities. Then get all in terms of sine only...eliminate cos[sup:1qy32vwv]2[/sup:1qy32vwv]x using cos[sup:1qy32vwv]2[/sup:1qy32vwv]x + sin[sup:1qy32vwv]2[/sup:1qy32vwv]x = 1.

  6. #6
    Elite Member
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    Re: prove sin3x=(sinx)(3-4sin^2x), solve sin3x=0, prove csc(x-y)

    Quote Originally Posted by bballbink
    i have a couple of problem here that have been giving me trouble if you can solve any of them that would be great!!

    Prove
    1. sin3x=(sinx)(3-4sin^2x)

    solve for all values in the interval (0-2pie)
    2. sin3x=0

    Prove
    3. csc(x-y)= sec y/ sinx-cosx tany
    Please show us your work, indicating exactly where you are stuck - so that we know where to begin to help you.
    “... mathematics is only the art of saying the same thing in different words” - B. Russell

  7. #7

    Re: prove sin3x=(sinx)(3-4sin^2x), solve sin3x=0, prove csc(x-y)

    Prove
    1. sin3x=(sinx)(3-4sin^2x)
    sin(2x+x)
    sin2x cosx+ cos2x sinx
    ?

    solve for all values in the interval (0-2pie)
    2. sin3x=0
    sin(2x+x)
    sin2x cosx+ cos2x sinx
    ?

    Prove
    3. csc(x-y)= sec y/ sinx-cosx tany

  8. #8
    Elite Member
    Join Date
    Jun 2007
    Posts
    12,863

    Re: prove sin3x=(sinx)(3-4sin^2x), solve sin3x=0, prove csc(x-y)

    Quote Originally Posted by bballbink
    Prove
    1. sin3x=(sinx)(3-4sin^2x)
    sin(2x+x)
    sin2x cosx+ cos2x sinx

    What did you get following Loren's advice?


    solve for all values in the interval (0-2pie)
    2. sin3x=0
    sin(2x+x)
    sin2x cosx+ cos2x sinx
    DUPLICATE POST

    viewtopic.php?f=10&t=32901

    Prove
    3. csc(x-y)= sec y/ sinx-cosx tany

    csc(x-y) = 1/sin(x-y)

    Now continue.....
    “... mathematics is only the art of saying the same thing in different words” - B. Russell

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