若cos(派/4+x)=3/5,17派/12
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若cos(派/4+x)=3/5,17派/12
若cos(派/4+x)=3/5,17派/12
若cos(派/4+x)=3/5,17派/12
17π/12＜x＜7π/4,得5π/3＜x+π/4＜2π
cos(x-π/4)=cos[(x+π/4)-π/2]=sin(x+π/4)=-√[1-cos²(x+π/4)]=-√[1-(3/5)²]=-4/5
sin(2x)=-cos(2x+π/2)=-cos[2(x+π/4)]=1-2cos²(x+π/4)=1-2•(3/5)²=7/25
[sin(2x)+2sin²x]/(1-tanx)
=2(sinxcosx+sin²x)/(1-sinx/cosx)
=2(cosx+sinx)/(1/sinx-1/cosx)
=2(cosx+sinx)sinxcosx/(cosx-sinx)
=cos(x-π/4)sin(2x)/cos(x+π/4)
=-4/5•7/25/(3/5)
=-28/75
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－sin...
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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
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