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解:
∵ π/2≤a<3π/2
∴ 3π/4≤a+π/4<7π/4
sin(a+π/4)=-√[1-cos²(a+π/4)]=-4/5
cos2a=sin[2(a+π/4)]=2sin(a+π/4)*cos(a+π/4)=-24/25
sin2a=-cos[2(a+π/4)]=1-2cos²(a+π/4)=7/25
tana=sina/cosa=2sina*cosa/(2cos²a)=sin2a/(1+cos2a)=7
故:
(1-cos2a+sin2a)/(1-tana)
=(1+24/25+7/25)/(1-7)
=-28/75
∵ π/2≤a<3π/2
∴ 3π/4≤a+π/4<7π/4
sin(a+π/4)=-√[1-cos²(a+π/4)]=-4/5
cos2a=sin[2(a+π/4)]=2sin(a+π/4)*cos(a+π/4)=-24/25
sin2a=-cos[2(a+π/4)]=1-2cos²(a+π/4)=7/25
tana=sina/cosa=2sina*cosa/(2cos²a)=sin2a/(1+cos2a)=7
故:
(1-cos2a+sin2a)/(1-tana)
=(1+24/25+7/25)/(1-7)
=-28/75
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