Use the composite argument formula cos (u-v)=cosucosv-sinusinv.
But first we need to find cos u and sin v. Since u is in Quadrant II and sin u= 3/5=(opposite)/(hypote n use we can find the adjacent side by using pythagorean theorem.
That is,
a^2=c^2-b^2
a=sqrt(5^2-3^2)=sqrt(25-9)=sqrt16=4 but since u is in quadrant two then a=-4. Hence, cos u=-4/5.
Likewise, we need to find sin v and v is in Quadrant III. So, to find the missing side from cos v= -5/6=(adjacent)/(hypote n use)
we use pythagorean theorem to find the length of the opposite side
o=sqrt(6^2-(-5)^2)=sqrt(36-25)=sqrt11. Since, v is in Quadrant III then o=-sqrt11 and sin v=-sqrt11/6
Therefore,
cos(u-v)=cosucosv-sinusinv
=(-4/5)(-5/6)-(3/5)(-sqrt11/6)
=((-2cancel4) /cancel5)(-cancel5/(3cancel6)-(cancel3/5)(-sqrt11/(2cancel6))
=2/3 + sqrt11/10
:.=(20+3sqrt11)/30