分子=2sinXcosX+(sinX)^2+(cosX)^2-((cosX)^2-(sinX)^2)
=2sinX(sinX+cosX)
=2sinXsin(X+π/4)*根号2
分母=(cosX-sinX)/cosX
=根号2*cos(π/4+X)/cosX
由题意得sin(π/4+X)=-4/5,sin2X=7/25代入得
分子/分母=-28/75
倍角公式的综合应用若cos(π/4+X)=3/5,17π/12
分子=2sinXcosX+(sinX)^2+(cosX)^2-((cosX)^2-(sinX)^2)
=2sinX(sinX+cosX)
=2sinXsin(X+π/4)*根号2
分母=(cosX-sinX)/cosX
=根号2*cos(π/4+X)/cosX
由题意得sin(π/4+X)=-4/5,sin2X=7/25代入得
分子/分母=-28/75