已知cos(75+α)=5/13,α是第三象限角,求sin(195-α)+cos(α-15)的值

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已知cos(75+α)=5/13,α是第三象限角,求sin(195-α)+cos(α-15)的值
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已知cos(75+α)=5/13,α是第三象限角,求sin(195-α)+cos(α-15)的值
已知cos(75+α)=5/13,α是第三象限角,求sin(195-α)+cos(α-15)的值

已知cos(75+α)=5/13,α是第三象限角,求sin(195-α)+cos(α-15)的值
cos(75+α)=cos(90-15+α)=cos[90+(α-15)]=-sin(α-15)=5/13
sin(α-15)=-5/13
cos(α-15)=±√[1 - sin^2 (α-15)]=±12/13
∵α是第三象限角且sin(α-15)<0
∴cos(α-15)=-12/13
sin(195-α) + cos(α-15)
=sin(180+15-α) + cos(α-15)
=sin[180-(α-15)] + cos(α-15)
=sin(α-15) + cos(α-15)
=-5/13 - 12/13
=-17/13

cos(75+α)=5/13,sin(15-α)=5/13,cos(15-α)=-12/13,sin(195-α)+cos(α-15)=-sin(15-α)+cos(α-15)=-17/13

∵cos(75°+α)=5/13,α是第三象限角,∴ sin(75°+α)=-12/13.
又∵cos(α-15)=cos[(75°+α)-90°]=cos[90°-(75°+α)]=sin(75°+α)=-12/13.
sin(195-α)=sin[270°-(75°+α)]=-cos(75°+α)=-5/13,

sin(195-α)+cos(α-15)= -5/13-12/13=-17/13