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trig

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Find the exact value by using a half-angle identity. cos 22.5 degrees

  • trig - ,

    use
    cos 2A = cos^2A - sin^2A
    cos2A = cos^2A - (1 - cos^2A) = 2cos^2A - 1
    cos 45° = 2cos^2 22.5° - 1
    √2/2 + 1 = 2cos^2 22.5
    √2/4 + 1/2 = cos^2 22.5°
    cos 22.5° = √[ (√2 + 2)/4 ]
    = √(√2 + 2) /2

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