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Math Help - sin(6x)/sin(2x) = sin(3x) ?

  1. #1
    s3a
    s3a is offline
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    sin(6x)/sin(2x) = sin(3x) ?

    Is

    sin(6x)/sin(2x) = sin(3x)

    ?

    If not, then what would be the correct way of expressing this?

    Any input would be greatly appreciated!
    Thanks in advance!
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  2. #2
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    e^(i*pi)'s Avatar
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    Quote Originally Posted by s3a View Post
    Is

    sin(6x)/sin(2x) = sin(3x)

    ?

    If not, then what would be the correct way of expressing this?

    Any input would be greatly appreciated!
    Thanks in advance!
    No, that is not right. A counterexample is x = \frac{\pi}{4}

    sin(6x) = sin(3 \times 2x) = 3sin(2x)+4sin^3(2x)

    <br />
\frac{3sin(2x)+4sin^3(2x)}{sin(2x)} = 3+4sin^2(2x)
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  3. #3
    Senior Member pacman's Avatar
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    sin(6x)/sin(2x) = sin(3x)

    (2sin 3x cos 3x)/sin 2x = sin 3x,

    that red thing (sin 2x) SHOULD be cos 3x, and 2 should be introduced to the RHS, to generate an identity. . . . see below

    (2sin 3x cos 3x)/cos 3x = 2 sin 3x
    Last edited by pacman; September 27th 2009 at 01:38 AM.
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