sin3Asin^3A+cos3Acos^3A 化简

绝颜羽衣2022-10-04 11:39:542条回答

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断刀流水1511 共回答了24个问题 | 采纳率95.8%: sin3a*sina^3+cos3a*cosa^3
=sin3a*sina*(sina)^2+cos3a*cosa*cosa^2
=1/2*(cos2a-cos4a)*(1-cosa^2)+1/2(cos2a+cos4a)*cosa^2
=1/2*[cos2a-cos4a-cos2a*cosa^2+cos4a*cosa^2+cos2a*cosa^2+ cos4a*cosa^2]
=1/2*[cos2a-cos4a+2cos4a*cosa^2]
=1/2*[cos2a-cos4a*(1-2cosa^2)]
=1/2*[cos2a+cos4a*cos2a]
=1/2*cos2a(1+cos4a)
=1/2*cos2a*(1+2cos2a^2-1)
=cos2a^3; 1年前

猫猫最怕打针共回答了127个问题 | 采纳率: ∵cos3A=4(cosA)^3-3cosA
sin3A=sin(2A+A)
=sin2AcosA+cos2AsinA
=2sinAcosAcosA+[1-2(sinA)^2]sinA
=sinA[2(cosA)^2+1-2(sinA)^2]sinA
=sinA[2-2(sinA)^2+1-2(sinA)^2]
=sinA[-4(sinA)^2+3]...; 1年前