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

Question

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

Answer 1

cos(75+a)=5/13,a是第三象限角
所以
75°+a是第四象限角
所以
sin(75+a)=-√1-cos²(75+a)=-12/13
sin(195-a)+cos(a-15)
=sin(180+15-a)+cos(a-15)
=-sin(15-a)+cos(a-15)
=sin(a-15)+cos(a-15)
=-cos(90°+(a-15°))+sin(90°+(a-15°))
=-cos(75+a)+sin(75+a)
=-5/13-12/13
=-17/13