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根三sinA CosA 化简

:(根号3)sina+_cosa=2(根号3/2*sina+1/2cosa)=2sin(a+30)

cosa根号下1-sina/1+sina 分子分母同时乘以 1-sina 分子=(1-sina)^2 分母=(1+sina)(1-sina)=1-sin^2a cosa根号下1-sina/1+sina =cosa根号下[(1-sina)^2/cos^2a]=cosa*(1-sina)/|cosa| cosa>0 =1-sina cosa

cosa+√3sina=2(1/2*cosa+√3/2*sina)=2(sin(π/6)cosa+cos(π/6)sina)=2sin(a+π/6)π

cosA-√3sinA=2(1/2cosA-√3/2sinA)=2(cos60°cosA-sin60°sinA)=2cos(A+60°)

sina+_(根号3)cosa=2(1/2*sina+根号3/2*cosa)=2sin(a+60)

√(2 2cosa) =√(2 2(2cos^2(a/2)-1) =√(4cos^2(a/2)) =-2cos(a/2) 1 sina cosa =1 2sin(a/2)cos(a/2) 2cos^2(a/2)-1 =2cosa/2*(sina/2 cosa/2) (1 sina cosa)(sina/2-cosa/2)/√(2 2cosa) =[2cosa/2*(sina/2 cosa/2)](sina/2-cosa/2)/(-2cosa/2) =-(sin^2a/2-cos^2a/2) =cosa

y=sina-√3cosa=2(1/2*sina-√3/2*cosa)=2(sinacosπ/3-cosasinaπ/3)=2sin(a-π/3)

sina + √3cosa =2[(1/2)sina + (√3/2)cosa] =2(sinacos60°+ cosasin60°) =2sin(a + 60°)

由公式sin2a=2sinacosa,cos2a=(cosa)^2-(sina)^2=1-2(sina)^2可得出sinacosa-√3/3(sina)^2=1/2sin2a-√3/3*(1-cos2a)/2=1/2sin2a+√3/6cos2a-√3/6

√3/2*sinA-1/2*cosA=1/2 sinAcosπ/6-cosAsinπ/6=1/2 sin(A-π/6)=1/2

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