sin(3a/2)*sin^3(a/2)+cos(3a/2)*cos^3(a/2)=?

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sin(3a/2)*sin^3(a/2)+cos(3a/2)*cos^3(a/2)=?

sin(3a/2)*sin^3(a/2)+cos(3a/2)*cos^3(a/2)=?
sin(3a/2)*sin^3(a/2)+cos(3a/2)*cos^3(a/2)=?

sin(3a/2)*sin^3(a/2)+cos(3a/2)*cos^3(a/2)=?
原式
=0.5*cosa*sin^2(a/2)-0.5*cos(2a)sin^2(a/2)+0.5*cos(2a)cos^2(a/2)+0.5*cosacos^2(a/2)（积化和差）
=0.5*cosa+0.5*cos(2a)cosa（二倍角公式）
=0.5*cosa*(1+cos(2a))
=0.5*cosa*(2cos^2(a))（二倍角公式）
=cos^3(a)

sin(3a/2)*sin^3(a/2)+cos(3a/2)*cos^3(a/2)
=-sin^2(a/2)[cos2a-cosa]/2-cos^2(a/2)[cos2a+cosa]/2
=cos2a[cos^2(a/2)-sin^2(a/2)]/2+cosa[cos^2(a/2)+sin^2(a/2)]/2
=cos2a*cosa/2+cosa/2
=cosa(cos2a+1)/2
=cosa^3

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