解方程 2sin^2x-3sinxcosx-2cos^2x=0

来源：学生作业帮编辑：作业帮分类：综合作业时间：2024/05/20 03:45:38

2sin^2x+5sinxcosx+cos^2x
=2sin^2x+5sinxcosx+(1-sin^2x)
=sin^2x+5sinxcosx+1
=-(1-2sin^2x-10sinxcosx-3)/2
=-(cos2x-5sin2x-3)/2=4
所以cos2x-5sin2x=-5
-√26*sin[2x+arctan(-1/5)]=-5
2x+arctan(-1/5)=2kπ+arcsin(5/√26)
或2x+arctan(-1/5)=2kπ+π-arcsin(5/√26)
所以x=[2kπ+arcsin(5/√26)+arctan(1/5)]/2
或x=[2kπ+π-arcsin(5/√26)+arctan(1/5)]/2
又arcsin(5/√26)+arctan(1/5)=π/2
-arcsin(5/√26)+arctan(1/5)=-arctan(12/5)
所以x=kπ+π/4
或x=[2kπ+π-arctan(12/5)]/2

解方程:sin^2x+2sinxcosx-3cos^3x=-2 方程sin^2x+2sinxcosx-2cos^2x-m=0恒有解 sin²X-sinxcosx+2cos²x= sin²x+sinxcosx+2cos²x= 若关于x的方程sin^x+2sinxcosx-2cos^x=a有实数解. 秒回答秒采纳 sin^2x-2sinxcosx-3cos^2x=0 已知函数f(x)=sin^x+根号3sinxcosx+2cos^x,x属于R 已知函数f(x)=cos^2x-sin^2x+2根号3sinxcosx+1 已知函数f(x)=根号3(sin^2x-cos^2x)-2sinxcosx 已知函数f（x）=sin^2x-2sinxcosx+3cos^2x 已知函数f(x)=sin^2x+2sinxcosx+3cos^2x 已知函数f（x）=sin^2x+2sinxcosx+3cos^x