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Math Help - simplify

  1. #1
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    simplify

    I want to go from  ac/(a^4sin^4(x)-c^2a^2sin^2(x))^{0.5} to cosec^2(x)/((a/c)^2-1-cot^2(x))^{0.5}
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  2. #2
    MHF Contributor Amer's Avatar
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    Re: simplify

    Quote Originally Posted by Duke View Post
    I want to go from  ac/(a^4sin^4(x)-c^2a^2sin^2(x))^{0.5} to cosec^2(x)/((a/c)^2-1-cot^2(x))^{0.5}
    \frac{ac}{\sqrt{a^4 \sin ^4 (x) - c^2 a^2 \sin ^2 (x)}}
    to
    \frac{csc ^2 (x)}{\sqrt{\frac{a^2}{c^2} -1 - \cot ^2 (x)}}

    you can divide the denominator and nominator by ac note ac = \sqrt{a^2c^2}
    take \sin ^4 (x) at the square root denominator as a factor
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  3. #3
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    Re: simplify

    I take sin^4(x) out and that helps numerator but I can't see the way forward.
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  4. #4
    MHF Contributor Siron's Avatar
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    Re: simplify

    We are given:
    \frac{ac}{\sqrt{a^4\sin^4(x)-c^2a^2\sin^2(x)}}

    Rewriting as:
    \frac{ac}{\sqrt{a^2c^2\sin^4(x)\left[\frac{a^2}{c^2}-\frac{1}{\sin^2(x)}\right]}}
    =\frac{ac}{ac\sin^2(x)\sqrt{\left(\frac{a}{c} \right)^2-\frac{\sin^2(x)+\cos^2(x)}{\sin^2(x)}}}
    =\frac{1}{\sin^2(x)\sqrt{\left(\frac{a}{c}\right)^  2-\frac{\sin^2(x)}{\sin^2(x)}-\frac{\cos^2(x)}{\sin^2(x)}}}
    =\frac{\csc^2(x)}{\sqrt{\left(\frac{a}{c}\right)^2-1-\cot^2(x)}}
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