Find the exact value of cos (u-v) given that sin u=-9/41 and cos v=15/17. (both u and v are in quadrant iv)

Please review the sum and difference formulas for the trig functions.

In this case you have the difference between two angles u and v and want to find the cosine of this difference.

Here's the appropriate formula:  

cos (a-b) = cos a cos b + sin a sin b

Given that sin u = -9/41, equal to the opp side over the hyp., we must find the length of the adj. side and then u itself.

opp side = - 9
hyp =           4
adj side = sqrt( 18+4) = sqrt(22)

Find the side opp angle v in a similar manner.

Then cos (u-v) = cos u cos v + sin u sin v becomes

                        = (cos u)(15/17) + (-9/41)(sin v)   (where you must find cos u and sin v)

See what you can do, then return and comment here if you need further help.  Good luck.