tanα=根号2，cos^2α/2-sinα-1比上根号2乘上sin(π/4+α)=

tanα=根号2，cos^2α/2-sinα-1比上根号2乘上sin(π/4+α)=

公式：
sin2x = 2sinx cosx
cos2x = cos²x - sin²x = 2cos²x - 1 = 1 - 2sin²x
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tanx = √2，x在 象限1 或 象限3
sinx/cosx = √2
sinx = √2 cosx
sin²x + cos²x = 1，代入上式
(√2 cosx)² + cos²x = 1
2cos²x + cos²x = 1
cos²x = 1/3
sin²x = 1 - 1/3 = 2/3
cos2x = 2cos²x - 1 = 2(1/3) - 1 = -1/3
sin2x = 2sinx cosx = 2(√2 cosx) cosx = 2√2 (1/3) = 2√2/3
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[cos²(x/2) - sinx - 1] / [√2 sin(π/4 + x)]
= [(1 + cosx) - sinx - 1] / [√2 (sin(π/4) cosx + cos(π/4) sinx)]
= (cosx - sinx) / [√2 (1/√2 cosx + 1/√2 sinx)]
= (cosx - sinx) / (cosx + sinx)
= (cosx - sinx)² / [(cosx + sinx)(cosx - sinx)]
= (cosx - sinx)² / (cos²x - sin²x)
= (1 - sin2x) / cos2x
= (1 - 2√2/3) / (-1/3)
= 2√2 - 3
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由于不知道x在 象限1 还是 象限3，所以过程中尽量不求出sinx和cosx的值。
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倒数第二步用的只是余弦的两倍角公式：cos2x = cos²x - sin²x
即 cosx = cos²(x/2) - sin²(x/2)