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trig

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use a half angle formula to find the exact value of cos 75 degree

  • trig -

    start with
    cos 2A = 2cos^2 A - 1

    cos150° = 2 cos^2 75 - 1
    -√3/2 + 1 = 2cos^2 75°
    cos^2 75° = (1 - √3/2)/2
    cos 75° = √[(1 - √3/2)/2]

    An easier ways would have been
    cos75 = cos(45+30)
    = cos45cos30 - sin45sin30
    = (1/√2)(√3/2) - (1/√2)(1/2)
    = (√3 - 1)/(2√2)

    Use your calculator to show that both produce cos75

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