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Math Help - exact value of sin 75^0

  1. #1
    rcs
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    exact value of sin 75^0

    can anybody let me know and understand why sin 75 deg. be equal this = (sq. rt of 6 + sq rt of 2)/4
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    Re: exact value of sin 75^0

    Hello, rcs!

    You are expected to know this identity:

    . . \sin(A+B) \:=\:\sin A\cos B + \sin B\cos A


    \text{Show that: }\:\sin(75^o) \:=\: \frac{\sqrt{6} + \sqrt{2}}{4}

    \sin(75^o) \;=\;\sin(45^o + 30^o)

    . . . . . . \;=\;\sin(45^o)\cos(30^o) + \sin(30^o)(\cos(45^o)

    . . . . . . =\;\left(\frac{1}{\sqrt{2}}\right)\left(\frac{ \sqrt{3}}{2}\right) + \left(\frac{1}{2}\right) \left(\frac{1}{\sqrt{2}}\right)

    . . . . . . =\;\frac{\sqrt{3}+1}{2\sqrt{2}}

    . . . . . . =\;\frac{\sqrt{3}+1}{2\sqrt{2}}\cdot{\color{blue} \frac{\sqrt{2}}{\sqrt{2}}}

    . . . . . . =\;\frac{\sqrt{6} + \sqrt{2}}{4}
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    rcs
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    Re: exact value of sin 75^0

    MILLIONS OF THANKS to Soroban you are a real genius with no hesitations ... thanks a lot soroban.
    Last edited by skeeter; September 15th 2012 at 05:54 PM. Reason: removed negative comments
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