Find the exact value of the trigonometric expression given t

Find the exact value of the trigonometric expression given that sin u = 8/17 and cos v = 3/5 . (Both u and v are in Quadrant II.) tan(u + v)

given sinu = 8/17

cosv =-3/5

given u,v are in QII

now from sin^2 u +cos^2 u=1

(8/17)^2 +cos^2 u =1

cos^2 u = 1 - 64/289

cos^2 u = 225/289

cosu = -15/17 (since u is in QII)

now tan u = sin u/cosu = (8/17)/ (-15/17)

tan u = -8/15

in the same find sinv value and tanv value

sin^2 v +cos^2 v=1

sin^2 v = 1 - (-3/5)^2

sin^2 v = 1 -9/25

sin^2 v =16/25

sinv =4/5 (since v is QII)

tanv = sin v/cosv =(4/5) /(-3/5)

tan v = -4/3

now tan(u+v) =( tanu + tanv) / (1 -tanu.tanv)

= ( -8/15 + -4/3 ) / (1 - (-8/15) (-4/3) )

= [ (-8 -12)/15 ] / [ (1- 32/45) ]

=(-20/15) /(13/45)

= (-20*3)/13

=-60/13