`cos(u + v)` Find the exact value of the trigonometric expression given that sin(u) = -7/25 and cos(v) = -4/5 (Both u and v are in quadrant III.)

Given `sin(u)=-7/25,cos(v)=-4/5`

Angles u and v are in quadrant 3.

A right triangle can be drawn in quadrant 3. Since `sin(u)=-7/25`  we know that the side opposite angle u is 7 and the hypotenuse is 25. Using the pythagorean theorem the third side of the triangle is 24.

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

`cos(u+v)=cos(u)cos(v)-sin(u)sin(v)`

`cos(u+v)=(-24/25)(-4/5)-(-7/25)(-3/5)=(96/125)-(21/25)=75/125=3/5`