已知sin(x/2)+cos(x/2)=1/2,则cos2x=?

来源:学生作业帮助网 编辑:六六作业网 时间:2024/12/26 13:11:29
已知sin(x/2)+cos(x/2)=1/2,则cos2x=?已知sin(x/2)+cos(x/2)=1/2,则cos2x=?已知sin(x/2)+cos(x/2)=1/2,则cos2x=?两边求平

已知sin(x/2)+cos(x/2)=1/2,则cos2x=?
已知sin(x/2)+cos(x/2)=1/2,则cos2x=?

已知sin(x/2)+cos(x/2)=1/2,则cos2x=?
两边求平方得:sin(x/2)^2+cos(x/2)^2+2sin(x/2)cos(x/2) = 1/4
--> 1+sin(x) = 1/4
--> sin(x)=-3/4
cos(2x) = 1-2sin(x)^2
= 1-2*(-3/4)^2
= -1/8

将已知两边平方可以1+sinx=1/4
于是sinx=-3/4
cos2x=1-2sin^2x=1-2·9/16=-1/8