已知cos(π/4+x)=-3/5,3/4π<x<5π/4,求(sin2x+2sin²x)/(1-tanx)的值.

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已知cos(π/4+x)=-3/5,3/4π<x<5π/4,求(sin2x+2sin²x)/(1-tanx)的值.

已知cos(π/4+x)=-3/5,3/4π<x<5π/4,求(sin2x+2sin²x)/(1-tanx)的值.
已知cos(π/4+x)=-3/5,3/4π<x<5π/4,求(sin2x+2sin²x)/(1-tanx)的值.

已知cos(π/4+x)=-3/5,3/4π<x<5π/4,求(sin2x+2sin²x)/(1-tanx)的值.
cos(π/4+x)
=cosπ/4cosx-sinπ/4sinx
=(√2/2)(cosx-sinx)
=-3/5
cosx-sinx=-3√2/5
(cosx-sinx)²=18/25
1-2sinxcosx=18/25
2sinxcosx=7/25
(sinx+cosx)²=1+2sinxcosx=1+7/25=32/25
又∵3/4π<x<5π/4
∴sinx+cosx