sin3x、cos3x等于好多?

sin3x、cos3x等于好多?
sin3x、cos3x等于好多?

sin3x、cos3x等于好多?
sin3a=3sina-4sin³a
cos3a =4cos³a-3cosa
推导方法如下：
sin3a
=sin(2a+a)
=sin2a×cosa+cos2a×sina
=2×sina×cosa×cosa+（1-2sin²a）×sina
=2sina×（1-sin²a）+（1-2sin²a）×sina
=2sina×(1-sin²a)+(1-2sin²a)×sina
=2sina-2sin³a+sina-2sin³a
=3sina-4sin³a
cos3a
=cos(2a+a)
=cos2a×cosa-sin2a×sina
=(2cos²a-1)×cosa-2×sina×cosa×sina
=(2cos²a-1)×cosa-2(sin²a)×cosa
=(2cos²a-1)cosa-2(1-cos²a)cosa
=2cos³a-cosa-2cosa+2cos³a
=4cos³a-3cosa

sin3a
=sin(2a+a)
=sin2acosa+cos2asina
=2sina(1-sin^2a)+(1-2sin^2a)sina
=3sina-4sin^3a

cos3a
=cos(2a+a)
=cos2a*cosa-sin2asina
=(2cosa^2-1)cosa-2sinacosasina
=(2cosa^2-1)cosa-2(sina^2)cosa
=(2cosa^2-1)cosa-2(1-cosa^2)cosa
=4cosa^3-3cosa