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Math Help - Am I doing this wrong?

  1. #1
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    Am I doing this wrong?

    I have to verify this identity algebraically:
    sin x (1 - 2 cos^2 x + cos^4 x) = sin^5 x

    So I have to make the left side equal the right,
    My work so far:
    sin x (sin^2 x cos^2 x + 4 coos x)
    sin x (sin^2 x [1 - sin^2 x] + 4 cos^4 x)
    sin x ([sin^2 x - sin^4 x] + 4 cos^4 x)
    sin x ([sin^2 x + cos^4 x + 1] + 4 cos^4 x)
    sin x (sin^2 x + 5 cos^4 x + 1)

    Now I am stuck. Am I correct so far? If I am, what do I do next?
    Any help is appreciated.
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  2. #2
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    skeeter's Avatar
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    Quote Originally Posted by iluvmathbutitshard View Post
    I have to verify this identity algebraically:
    sin x (1 - 2 cos^2 x + cos^4 x) = sin^5 x

     <br />
\sin{x}\textcolor{red}{(1 - \cos^2{x})^2} = \sin^5{x}<br />
    continue ...
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  3. #3
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    sin x (1 - cos^2 x^2)^2
    sin x (sin^2 x) (sin^2 x)
    is this correct?
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  4. #4
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    Just in case, you should know this...

    \sin^2\theta + \cos^2\theta = 1

    From this other things can be derived and it will help you with trig identities.
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  5. #5
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    Hello iluvmathbutitshard
    Quote Originally Posted by iluvmathbutitshard View Post
    sin x (1 - cos^2 x^2)^2 You don't need the bit in red.
    sin x (sin^2 x) (sin^2 x)
    is this correct?
    Yes, more or less (see above). And this, of course, gives \sin^5x.

    Grandad
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  6. #6
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    Thank you so much.
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