Question

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

Answer 1

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