To solve the the question we proceed as follows: From trigonometric laws (cos x)^2+(sin x)^2=1 (cos y)^2+(sin y)^2=1 sin (x-y)=sin x sin y-sin y cos x cos (x-y)=cos x cos y+ sin x sin y si x=8/17 cos x=sqrt(1-(sin x)^2)=sqrt(1-64/289)=sqrt(225/289)=15/17 cos y=3/5 sin x= sqrt(1- (cos x)^2)= sqrt(1-9/25)=sqrt(16/25)=4/5 thus tan (x-y)=[sin (x-y)]/[cos (x-y)] =[sin x cos y-sin y cos x]/[cos x cos y+sin x sin y] plugging in the values we obtain: [8/17 *3/5-4/5*15/7]/[15/17*3/5+8/17*4/5] simplifying [24/85-60/85]/[45/85+32/85] =-36/77
