已知(2sin^2x+sin2x)/(1+tanx)=1/2(π/4

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已知(2sin^2x+sin2x)/(1+tanx)=1/2(π/4

已知(2sin^2x+sin2x)/(1+tanx)=1/2(π/4
已知(2sin^2x+sin2x)/(1+tanx)=1/2(π/4

已知(2sin^2x+sin2x)/(1+tanx)=1/2(π/4
(2sin^2x+sin2x)/(1+tanx)
=cosx*(2sin^2x+2cosx*sinx)/(1+tanx)*cosx
=2sinx*cosx(sinx+cosx)/(cosx+sinx)
=2sinx*cosx=sin2x=1/2
(sinx-cosx)^2=sin^2x+cos^2x+2sinxcosx
=1+sin2x=3/2
π/40
sinx-cosx=√(3/2)