已知：cos3α=4 (cosα)^3-3cosα,类似地用sin α/3表示sinα,并证明
问题描述：
已知：cos3α=4 (cosα)^3-3cosα,类似地用sin α/3表示sinα,并证明
答
sina=3sin(a/3)--4[sin(a/3)]^3.证明：sina=sin(2a/3+a/3)=sin(2a/3)cos(a/3)+cos(2a/3)sin(a/3)=2sin(a/3)[cos(a/3)]^2+{1--2[sin(a/3)]^2}sin(a/3)=2sin(a/3){1--[sin(a/3)]^2}+{sin(a/3)--2[sin(a/3)]^3}=2sin(a/...