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Math Help - basic simplification question

  1. #1
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    basic simplification question

    is this right?

    \frac{cos(x)}{(cos^4(x))^{\frac{3}{2}}} = cos^{-5}(x)
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  2. #2
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    Looks good to me. Just a matter of using your power laws.
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  3. #3
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    Looks good to me too.
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  4. #4
    Behold, the power of SARDINES!
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    Quote Originally Posted by lllll View Post
    I need some help simplifying:

    \frac{cos(x)}{(cos^2(x))^{\frac{3}{2}}}

    Thanks in advance.

    (\cos^2(x))^{3/2}=|cos(x)|^3

    so we get

    \begin{cases}<br />
\sec^2(x) \mbox{if }-\frac{\pi}{2} < x < \frac{\pi}{2} \\<br />
-\sec^2(x) \mbox{if } \frac{\pi}{2} < x < \frac{3\pi}{2}<br />
\end{cases}
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  5. #5
    Behold, the power of SARDINES!
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    (\cos^4(x))^{3/2}=|cos(x)|^6

    Dont forget that

    \sqrt{x^2}=|x|

    example x=-2

    Yours should be

    \frac{1}{|\cos(x)|\cos^4(x)}

    try  x=\pi
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