化简[1-(sin^4 x-sin^2 xcos^2 x+cos^4 x)]/(sin^2 x)+3sin^2 x

来源:学生作业帮助网 编辑:作业帮 时间:2024/03/29 20:20:04
化简[1-(sin^4 x-sin^2 xcos^2 x+cos^4 x)]/(sin^2 x)+3sin^2 x

化简[1-(sin^4 x-sin^2 xcos^2 x+cos^4 x)]/(sin^2 x)+3sin^2 x
化简[1-(sin^4 x-sin^2 xcos^2 x+cos^4 x)]/(sin^2 x)+3sin^2 x

化简[1-(sin^4 x-sin^2 xcos^2 x+cos^4 x)]/(sin^2 x)+3sin^2 x
注意到sin^2x+cos^2x=1
所以1=(sin^2x+cos^2x)^2=sin^4 x+2sin^2 xcos^2 x+cos^4 x
1-3sin^2 xcos^2 x=sin^4 x-sin^2 xcos^2 x+cos^4 x

[1-(sin^4 x-sin^2 xcos^2 x+cos^4 x)]/(sin^2 x)+3sin^2 x=(3sin^2 xcos^2 x)/(sin^2 x)+3sin^2 x
=3cos^2x+3sin^2x=3

【1-((sin^2x+cos^2x)^2-2sin^2xcos^2x-2sin^2xcos^2x)】/(sin^2 x)+3sin^2 x
=【1-1+3sin^2xcos^2x】/(sin^2 x)+3sin^2 x
=3sin^2xcos^2x/sin^2 x+3sin^2 x
=3COS^2X+3sin^2
=3(sin^2x+cos^2x)
=3