急!!!高一数学三角函数填空!!!!!

来源:百度知道 编辑:UC知道 时间:2024/05/14 09:27:17
若cos(π/4+x)=3/5 (17π/12)<x<(7π/4) 则(sin2x+2sin^2x)/(1-tanx)等于
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π/4+x的范围是5π/3<π/4+x<2π 角度在第四象限
根据cos(π/4+x)=3/5
得出sin(π/4+x)=-4/5

sinx+cosx=√2sin(π/4+x)=-4√2/5

(sinx+cosx)^2=32/25 所以2sinxcosx=(sinx+cosx)^2-1=7/25

cosx-sinx=√2cos(π/4+x)=3√2/5

(sin2x+2sin^2x)/(1-tgx)
=( 2sinxcosx+2sin^2x)/(1-sinx/cosx)
=2sinx(cosx+sinx)/ (1-sinx/cosx)
=2sinxcosx(cosx+sinx)/(cosx-sinx)
=-28/75 (把上面的计算结果带进去,求得最后结果)

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