`tan(u + v)` Find the exact value of the trigonometric expression given that sin(u) = 5/13 and cos(v) = -3/5 (both u and v are in quadrant II.)

Given `sin(u)=5/13,cos(v)=-3/5`

Angles u and v are in quadrant 2.

A right triangle can be drawn in quadrant 2. Since `sin(u)=5/13`    we know that the side opposite angle u is 5 and the hypotenuse of the triangle is 13. Using the pythagorean theorem the third side of the triangle is 12.

A second triangle can be drawn in quadrant 2. Since `cos(v)=-3/5` we know that the side adjacent angle v is 3 and the hypotenuse of the triangle is 5. Using the pythagorean theorem the third side of the triangle is 4.

`tan(u+v)=(tan(u)+tan(v))/(1-tan(u)tan(v))`

`tan(u+v)=((-5/12)+(-4/3))/(1-(-5/12)(-4/3))=((-5+(-16))/12)/(1-(20/36))=(-21/12)/(16/36)=-63/16`