作业帮(1+cos x-sin x)/(1-sin x-cos x)+(1-cos x-sin x)/(1-sin x+cos x)=?
来源：学生作业帮助网 编辑：作业帮 时间：2024/11/21 02:30:41
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(1+cos x-sin x)/(1-sin x-cos x)+(1-cos x-sin x)/(1-sin x+cos x)=?
(1+cos x-sin x)/(1-sin x-cos x)+(1-cos x-sin x)/(1-sin x+cos x)=?
(1+cos x-sin x)/(1-sin x-cos x)+(1-cos x-sin x)/(1-sin x+cos x)=?
原式=((1+cosx-sinx)^2+(1-cosx-sinx)^2)/((1-sinx-cosx)(1-sinx+cosx))
=（1+sin^2(x)+cos^2(x)-2sinx+2cosx-2sinxcosx+1+sin^2(x)+cos^2(x)-2sinx-2cosx+2sinxcosx）/((1-sinx)^2-cos^2(x))
=(4-4sinx)/(2sinx(sinx-1))
当x=2kπ+π/2（k为整数）时,原式无意义
当x≠2kπ+π/2（k为整数）时,原式=-2/sinx
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