Find the exact value of tan u v given that sin u 941 and c

Find the exact value of tan (u + v) given that sin u = -9/41 and cos v = 15/17. (Both u and v are in Quadrant IV.) -455/528 97/264 221/528 37/33 None of these

Solution

sin u = -9/41

base = sqrt ( 41^2 - 9^2 ) = 40

tan u = - 9 / 40

cos v = 15 / 17

perpendicular = sqrt (17^2 - 15^2 ) = 8

tan v = - 8/15

tan ( u + v)

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

= ( -9/40 - 8/15 ) / ( 1 - 9/40 * 8/15 )

= ( - 135 - 320 ) / 600 / 528 / 600

= - 455 / 528

option a is correct