三角比化简~cos^2(A+15°)+sin^2(A-15°)+sin(A+180°)cos(A-180°)3Q
来源:学生作业帮助网 编辑:作业帮 时间:2024/07/11 16:29:55
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三角比化简~cos^2(A+15°)+sin^2(A-15°)+sin(A+180°)cos(A-180°)3Q
三角比化简~
cos^2(A+15°)+sin^2(A-15°)+sin(A+180°)cos(A-180°)
3Q
三角比化简~cos^2(A+15°)+sin^2(A-15°)+sin(A+180°)cos(A-180°)3Q
sin(A+180°)cos(A-180°)
=(-sinA)*(-cosA)
=sinAcosA
cos^2(A+15°)+sin^2(A-15°)
=cos^2(A+15°)+sin^2(A+15°)-sin^2(A+15°)+sin^2(A-15°)
=1-sin^2(A+15°)+sin^2(A-15°)
-sin^2(A+15°)+sin^2(A-15°)
=[sin(A-15°)+sin(A+15°)][sin(A-15°)-sin(A+15°)]
=2[sinAcos15]*2[cosAsin(-15)]
=-4sin15cos15sinAcosA
=-2sin30sinAcosA
=-sinAcosA
所以cos^2(A+15°)+sin^2(A-15°)
=1-sinAcosA
所以原式=1
cos^2(A+15°)+sin^2(A-15°)+sin(A+180°)cos(A-180°)
=[cos2(A+15°)+1]/2+[1-cos2(A-15°)]/2+sinA*cosA
=[cos2(A+15°)-cos2(A-15°)]/2+sin2A/2
=-sinA/2+sinA/2
=0
里面化简有个和差化积的公式:
cosθ-cos...
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cos^2(A+15°)+sin^2(A-15°)+sin(A+180°)cos(A-180°)
=[cos2(A+15°)+1]/2+[1-cos2(A-15°)]/2+sinA*cosA
=[cos2(A+15°)-cos2(A-15°)]/2+sin2A/2
=-sinA/2+sinA/2
=0
里面化简有个和差化积的公式:
cosθ-cosφ=-2sin[(θ+φ)/2]sin[(θ-φ)/2]
其他和差化积,积化和差公式
积化和差公式:
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
和差化积公式:
sinθ+sinφ=2sin[(θ+φ)/2]cos[(θ-φ)/2]
sinθ-sinφ=2cos[(θ+φ)/2]sin[(θ-φ)/2]
cosθ+cosφ=2cos[(θ+φ)/2]cos[(θ-φ)/2]
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