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Math Help - complex no.

  1. #1
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    complex no.

    p302 q13
    prove that 16cos^4x sin x = sin 5x +3sin3x+2sinx
    my working:
    let
    z = cos x + i sin x
    z + 1/z = cos x
    z - 1/z = i sin x
    i can only prove 16cos^4x sin x = 16 ( sin 5x + 3 sin 3x + 2sinx) 2i
    what's wrong?
    thanks
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  2. #2
    Moo
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    Yop,

    Quote Originally Posted by afeasfaerw23231233 View Post
    p302 q13
    prove that 16cos^4x sin x = sin 5x +3sin3x+2sinx
    my working:
    let
    z = cos x + i sin x
    z + 1/z ={\color{red}2} cos x
    z - 1/z ={\color{red}2} i sin x
    i can only prove 16cos^4x sin x = 16 ( sin 5x + 3 sin 3x + 2sinx) 2i
    what's wrong?
    thanks
    Same mistake as in one of your previous threads (in red)



    Though I have no time at the moment to check if your method will yield the thing we want, because of i.. ^^'
    Last edited by Moo; May 20th 2008 at 11:46 AM.
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  3. #3
    MHF Contributor Mathstud28's Avatar
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    Quote Originally Posted by afeasfaerw23231233 View Post
    p302 q13
    prove that 16cos^4x sin x = sin 5x +3sin3x+2sinx
    my working:
    let
    z = cos x + i sin x
    z + 1/z = cos x
    z - 1/z = i sin x
    i can only prove 16cos^4x sin x = 16 ( sin 5x + 3 sin 3x + 2sinx) 2i
    what's wrong?
    thanks
    16\cos^4(x)\sin(x)=16\bigg(\frac{e^{ix}+e^{-ix}}{2}\bigg)^4\cdot\bigg(\frac{e^{ix}-e^{-ix}}{2}\bigg)


    That is generally how I start all of these problems. In this case it may not be as useful but it usually helps
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