Cos(arccos 12/13-arcsin 8/17)

Question

Cos(arccos 12/13-arcsin 8/17)

Answer 1

Cos(x-y)=cosx*cosy + sinx*siny
cos(arcsinx)=sin(arccosx)=√(1-x²)
Cos(arccos 12/13-arcsin 8/17)=cos(arccos(12/13))*cos(arcsin(8/17)) + sin(arccos(12/13))*sin(arcsin(8/17)) = 12/13*√(1-(8/17)²) + √(1-(12/13)²)* 8/17 = 12/13*15/17 + 5/13*8/17 = 220/221