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Math Help - Deduce the value in surd form

  1. #1
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    Deduce the value in surd form

    If A=36^o, show that \sin 3A= \sin 2A, and deduce that \cos 36^o=\frac{\sqrt{5}+1}{4}

    I have already shown \sin 3A= \sin 2A when A=36^o, since 108^o=180^o-72^o.
    But I don't know how to deduce that \cos 36^o=\frac{\sqrt{5}+1}{4}.
    Thanks!
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  2. #2
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    Hello arze
    Quote Originally Posted by arze View Post
    If A=36^o, show that \sin 3A= \sin 2A, and deduce that \cos 36^o=\frac{\sqrt{5}+1}{4}

    I have already shown \sin 3A= \sin 2A when A=36^o, since 108^o=180^o-72^o.
    But I don't know how to deduce that \cos 36^o=\frac{\sqrt{5}+1}{4}.
    Thanks!
    Four steps:

    • Use the identities \sin2A=2\sin A \cos A and \sin3A=3\sin A -4\sin^3A in the equation \sin 3A= \sin 2A


    • Divide through by \sin A (it's non-zero, so that's OK)


    • Replace \sin^2A by 1 - \cos^2A


    • Solve the quadratic for \cos A, taking the positive root.

    Can you complete it now?

    Grandad
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  3. #3
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    Yes! i can complete it now! thanks
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