so you want sin π/8 or sin 22.5° recall that cos 2A = 1 - 2sin^2 A then cos 45° = 1 - 2sin^2 2.5° 2sin^2 22.5° = 1 - cos45° = 1 - √2/2 = (2 - √2)/2 sin^2 22.5 = (2 - √2)/4 sin 22.5 = sin π/8= √(2 - √2) / 2
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