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sinx Cosx

sinx+cosx =√2(√2/2sinx+√2/2cosx) =√2(sinxcos45+cosxsin45) =√2sin(x+45) 注:45 是45度

由2倍角定理。sin2x=2sinx*cosx.所以sinx*cosx=1/2sin2x.

提取一个√2

这样?

进行凑微分即可, 得到原积分 =∫ 1/√(sinx-cosx) d(sinx-cosx) = ∫(sinx-cosx)^(-1/2) d(sinx-cosx) = 2(sinx-cosx)^(1/2) +C = 2√(sinx-cosx) +C,C为常数

sinx/cosx + cosx/sinx = 4 sin²x/(sinxcosx) + cos²x/(sinxcosx) = 4 (sin²x + cos²x)/(sinxcosx) = 4 1/(sinxcosx) = 4 sinxcosx = 1/4 sin2x = 1/2 2x = 2kπ + π/6 或2kπ + 5π/6 x = kπ + π/12 或 kπ + 5π/12 ,k ∈Z

sinx+cosx=√2sin(x+π/4)=0 sin(x+π/4)=0 x+π/4=2kπ或2kπ+π,k∈Z x=2kπ-π/4或2kπ+3π/4,k∈Z

∫sinxcosxdx =∫sinxd(sinx) =½sin²x+C

-sinx=cos(X+π/2) -SINX=COS(X+3π/2) COSX=SIN(X+π/2) COSX=SIN(X+3π/2)

解:利用零点分区去绝对值 ①由sinx-cosx>0得 √2sin(x-π/4)>0 解得 2kπ

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