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(1+cosx-sinx)/(1-cosx-sinx)+(1-cosx-sinx)/(1+cosx-sinx)
=[(1+cosx-sinx)(1+cosx+sinx)]/[(1-cosx-sinx)(1+cosx+sinx)]
+[(1-cosx-sinx)(1-cosx+sinx)]/[(1+cosx-sinx)(1-cosx+sinx)]
=(1+2cosx+cos2x)/(-sin2x)+(1-2cosx+cos2x)/(sin2x)
=(-4cosx)/sin2x
=-2/sinx
2)若tan(x/2)*(-2/sinx)=[1+tan^2(x/2)]/sinx＝>
tan^2(x/2)+2tan(x/2)+1=0 =>[tan(x/2)+1]^2=0 =>tan(x/2)=-1
=>x/2=kpai-pai/4 =>x=2kpai-pai/2
=[(1+cosx-sinx)(1+cosx+sinx)]/[(1-cosx-sinx)(1+cosx+sinx)]
+[(1-cosx-sinx)(1-cosx+sinx)]/[(1+cosx-sinx)(1-cosx+sinx)]
=(1+2cosx+cos2x)/(-sin2x)+(1-2cosx+cos2x)/(sin2x)
=(-4cosx)/sin2x
=-2/sinx
2)若tan(x/2)*(-2/sinx)=[1+tan^2(x/2)]/sinx＝>
tan^2(x/2)+2tan(x/2)+1=0 =>[tan(x/2)+1]^2=0 =>tan(x/2)=-1
=>x/2=kpai-pai/4 =>x=2kpai-pai/2
追答
(1+cosx-sinx)/(1-cosx-sinx)+(1-cosx-sinx)/(1+cosx-sinx)
=[(1+cosx-sinx)(1+cosx+sinx)]/[(1-cosx-sinx)(1+cosx+sinx)]
+[(1-cosx-sinx)(1-cosx+sinx)]/[(1+cosx-sinx)(1-cosx+sinx)]
=(1+2cosx+cos2x)/(-sin2x)+(1-2cosx+cos2x)/(sin2x)
=(-4cosx)/sin2x
=-2/sinx
2)若tan(x/2)*(-2/sinx)=[1+tan^2(x/2)]/sinx＝>
tan^2(x/2)+2tan(x/2)+1=0 =>[tan(x/2)+1]^2=0 =>tan(x/2)=-1
=>x/2=kpai-pai/4 =>x=2kpai-pai/2
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