2sinx^2-sinxcosx-3cosx^2=0 求sin(x+45)/(sin2x+cos2x+1)

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2sinx^2-sinxcosx-3cosx^2=0 求sin(x+45)/(sin2x+cos2x+1)
2sinx^2-sinxcosx-3cosx^2=0 求sin(x+45)/(sin2x+cos2x+1)

2sinx^2-sinxcosx-3cosx^2=0 求sin(x+45)/(sin2x+cos2x+1)
sin(x+45)/(sin2x+cos2x+1)
=(sinx*cos45+sin45*cosx)/(2sinx*cosx+2cosx*cosx)
=(sinx+cosx)/2cosx*(sinx+cosx)
=1/2cosx
2sinx^2-sinxcosx-3cosx^2=0
(2sinx+cosx)(sinx-3cosx)=0
所以2sinx=-cosx或sinx=3cosx
则cosx=(根号5)/5,或cosx=(3倍根号10)/10
再代入就是了