trig

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2cos^2 22.5-1 (find exact value)

  • trig -

    cos^2 θ/2 = (1 + cosθ)/2

    cos^2 22.5° = (1 + cos 45°)/2
    = (1 + √2/2)/2
    = (2 + √2)/4

  • trig -

    hmmph

    It would help to notice that

    2cos^2 θ - 1 = cos 2θ

    so what you have is just cos 45° = 1/√2

    note that 2(2+√2)/4 - 1 = 1+√2/2-1 = √2/2 = 1/√2

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