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Math Help - inverse trigonometry

  1. #1
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    inverse trigonometry

    Show that 2sin-1(3/5) = sin-1(24/25)

    any help is greatly appreciated ! thankyou !
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  2. #2
    MHF Contributor Amer's Avatar
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    Quote Originally Posted by iiharthero View Post
    Show that 2sin-1(3/5) = sin-1(24/25)

    any help is greatly appreciated ! thankyou !
    it is the first time I solved something like this


    \sin ^{-1} \left(\frac{3}{5}\right) = u

     \frac{3}{5} = \sin u

    inverse trigonometry-inverse.jpg

    \cos u = \frac{4}{5}

    \sin u \cos u = \frac{3}{5}\left(\frac{4}{5}\right)

    \sin u \cos u = \frac{12}{25}

    \frac{\sin 2u }{2} = \frac{12}{25}

    \sin 2u = \frac{24}{25}

    2u=\sin ^{-1} \left(\frac{24}{25}\right)

    but
    u=\sin ^{-1} \left(\frac{3}{5}\right)

    2\sin ^{-1} \left(\frac{3}{5}\right)=\sin ^{-1} \left(\frac{24}{25}\right)
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  3. #3
    MHF Contributor alexmahone's Avatar
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    Let \frac{3}{5}=sin\theta

    cos\theta=\frac{4}{5}

    sin2\theta=2sin\theta cos\theta

    sin2\theta=2*\frac{3}{5}*\frac{4}{5}

    sin2\theta=\frac{24}{25}

    2\theta=sin^{-1}{\frac{24}{25}}

    2sin^{-1}{\frac{3}{5}}=sin^{-1}{\frac{24}{25}}
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