Question

How do you evaluate the expression `tan(u+v)` given `sinu=3/5` with `pi/2<u<p` and `cosv=-5/6` with `pi<v<(3pi)/2`?

Answer 1

`=(432+125sqrt11)/301`

Explanation:

`tan(u+v)=(sin(u+v))/cos(u+v)=(sinucosv+cosusinv)/(cosucosv-sinusinv)`

`cosu=sqrt(1-(3/5)^2)=4/5`

`sinv=-sqrt(1-(-5/6)^2)=-sqrt11/6`
"-" becose v in third quarter

`((3/5)*(-5/6)+(4/5)*(-sqrt11/6))/((4/5)*(-5/6)-(3/5)*(-sqrt11/6))`

`=(-1/2-2sqrt11/15)/(-2/3+sqrt11/10)=(15+4sqrt11)/(20-3sqrt11)`

`=(432+125sqrt11)/301`