sin(x/2) - cos(x/2)=1 求x的解集?

来源：百度知道编辑：UC知道时间：2024/05/13 13:27:10

要过程的.

sin(x/2) - cos(x/2)=根号2倍sin(x/2- pai/4)=1
则sin(x/2- pai/4)=根号2/2
故x/2- pai/4=pai/4 + 2k*pai,或x/2- pai/4=3*pai/4 + 2k*pai
,因此
x=(4k+1)pai,或x=(4k+2)pai,也即4k*pai,
k属于Z

画图

sin(x/2) - cos(x/2)=1 两边平方得
2sin(x/2)*cos(x/2)=0 即sinx=0
故x=kπ
k为整数

sin(x/2)-cos(x/2)=1
(sin(x/2)-cos(x/2))^2=1
sin(x/2)^2+cos(x/2)^2-2sin(x/2)cos(x/2)=1
1-2sin(x/2)cos(x/2)=1
1-sinx=1
-sinx=0
sinx=0

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