三角函数的积化和差和差化积公式

Question

如题所述

Answer 1

和差化积
cos(α+β)=cosαcosβ-sinαsinβ cos(α-β)=cosαcosβ+sinαsinβ sin(α+β)=sinαcosβ+cosαsinβ sin(α-β)=sinαcosβ -cosαsinβ
积化和差
sinαsinβ = [cos(α-β)-cos(α+β)] /2 cosαcosβ = [cos(α+β)+cos(α-β)]/2 sinαcosβ = [sin(α+β)+sin(α-β)]/2 cosαsinβ = [sin(α+β)-sin(α-β)]/2

Answer 2

和差化积：sinθ-sinφ=2cos(θ/2+φ/2)sin(θ/2-φ/2)
cosθ+cosφ=2cos(θ/2+φ/2)cos(θ/2-φ/2)
cosθ-cosφ=-2sin(θ/2+φ/2)sin(θ/2-φ/2)
积化和差：sinαsinβ=-[cos(α+β)-cos(α-β)]/2 　
　 cosαcosβ=[cos(α+β)+cos(α-β)]/2 　
　 sinαcosβ=[sin(α+β)+sin(α-β)]/2 　
　 cosαsinβ=[sin(α+β)-sin(α-β)]/2

Answer 3

和差化积：sinθ-sinφ=2cos(θ/2 φ/2)sin(θ/2-φ/2)
cosθ cosφ=2cos(θ/2 φ/2)cos(θ/2-φ/2)
cosθ-cosφ=-2sin(θ/2 φ/2)sin(θ/2-φ/2)
积化和差：sinαsinβ=-[cos(α β)-cos(α-β)]/2 　
　 cosαcosβ=[cos(α β) cos(α-β)]/2 　
　 sinαcosβ=[sin(α β) sin(α-β)]/2 　
　 cosαsinβ=[sin(α β)-sin(α-β)]/2

Answer 4

Answer 5

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