sinx-cosx可以怎么化
\u5316\u7b80:(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-cosx-sinx)(1-cosx+sinx)]/[(1+cosx-sinx)(1-cosx+sinx)]
=(1+2cosx+cos2x)/(-sin2x)+(1-2cosx+cos2x)/(sin2x)
=(-4cosx)/sin2x
=-2/sinx
\uff08sinx+cosx\uff09*\uff08sinx+cosx\uff09+sinx-cosx*cosx
=\uff08sinx\uff09^2+\uff08cosx\uff09^2+2sinxcosx+sinx-cosx*cosx
=\uff08sinx\uff09^2+2sinxcosx+sinx
=\uff08sinx\uff09^2+sin2x+sinx
=√2sin(x－π/4)
2sinxcosx+sinx-cosx=1 =>
sinx-cosx=cosx^2+sinx^2-2sinxcosx=(sinx-cosx)^2 =>
sinx-cosx=√2sin(x－π/4) =0或1
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