sin(x/2)﹣ cos(x/2)= 更号2

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sin(x/2)﹣cos(x/2)=更号2sin(x/2)﹣cos(x/2)=更号2sin(x/2)﹣cos(x/2)=更号2[sin(x/2)-cos(x/2)]²=sin²(x

sin(x/2)﹣ cos(x/2)= 更号2
sin(x/2)﹣ cos(x/2)= 更号2

sin(x/2)﹣ cos(x/2)= 更号2
[sin(x/2)-cos(x/2)]²=sin²(x/2)+cos²(x/2)-2sin(x/2)cos(x/2)=1-sin(2*x/2)=2
sinx=-1
x=3π/2+2kπ,k∈整数

将sin(x/2)﹣cos(x/2)= 更号2两边同时平方得:
sin²(x/2)-2sin(x/2)cos(x/2)+cos²(x/2)=2.
得:sin²(x/2)+cos²(x/2)-sinx=2.
得:-sinx=1,则sinx=-1,则x=arcsin-1,得x=-90º(270º)

sin(x/2)-cos(x/2)=根号2
两边平方得:1-2sin(x/2)cos(x/2)=2
化简得:sin(x/2)cos(x/2)=-1/2 (1)
由sin(x/2)-cos(x/2)=根号2
得:sin(x/2)=根号2+cos(x/2) ...

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sin(x/2)-cos(x/2)=根号2
两边平方得:1-2sin(x/2)cos(x/2)=2
化简得:sin(x/2)cos(x/2)=-1/2 (1)
由sin(x/2)-cos(x/2)=根号2
得:sin(x/2)=根号2+cos(x/2) (2)
把(2)代入(1)得:1+根号2cos(x/2)=0
故cos(x/2)=-根号2/2
因此解得X=3π/4或5π/4
愿我的解答能够解决你的问题~

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