Trig

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How do we show (sin 10)^2 + (sin 50)^2 + (sin 70)^2 = 3/2 ???
I can't even think of a way to start this..

  • Trig -

    since sin^2θ = (1-cos2θ)/2, we have

    (1-cos20)/2 + (1-cos100)/2 + (1-cos140)/2 = 3/2
    cos20+cos100+cos140 = 0

    Using the sum-to-product rules,

    cos20 + cos100+cos140
    = cos20 + 2cos120cos20
    = cos20 - cos20
    = 0

  • Trig -

    Thank you very much Steve

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