化简(sin^2 x/sin x-cosx)-(sin x+cosx/tan^2 x-1)
来源:学生作业帮助网 编辑:作业帮 时间:2024/05/15 11:03:32
化简(sin^2 x/sin x-cosx)-(sin x+cosx/tan^2 x-1)
化简(sin^2 x/sin x-cosx)-(sin x+cosx/tan^2 x-1)
化简(sin^2 x/sin x-cosx)-(sin x+cosx/tan^2 x-1)
tan²-1=sin²x/cos²x-1=(sin²x-cos²x)/cos²x=(sinx+cosx)(sinx-cosx)/cos²x
所以(sinx+cosx)/(tan²-1)=(sinx+cosx)/[(sinx+cosx)(sinx-cosx)/cos²x]
=cos²x/(sinx-cosx)
所以原式=sin²x//(sinx-cosx)-cos²x/(sinx-cosx)
=(sin²x-cos²x)/(sinx-cosx)
=(sinx+cosx)(sinx-cosx)/(sinx-cosx)
=sinx+cosx
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