sin(3a/2)*sin^3(a/2)+cos(3a/2)*cos^3(a/2)=?
问题描述：
sin(3a/2)*sin^3(a/2)+cos(3a/2)*cos^3(a/2)=?
答
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
答
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...