已知cos(π/4+α)=3/5,(17π)/12

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已知cos(π/4+α)=3/5,(17π)/12
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已知cos(π/4+α)=3/5,(17π)/12
已知cos(π/4+α)=3/5,(17π)/12

已知cos(π/4+α)=3/5,(17π)/12
(17π)/12

5π/3<π/4 +α<2π,
sin(π/4 +α)=-4/5,①
cos(π/4+α)=3/5,②
①与②相乘可得
sin(π/2+2α)=-24/25.
Cos2α=-24/25,
又2π+5π/6<2α<2π+3π/2
sin2α=-7/25.
①与②相除可得
tan(π/4+α)=-4/3.
[sin2α(1+tanα)]/(1-tanα)
=sin2αtan(π/4+α)
=-7/25×(-4/3)
=28/75.