Find the Exact Value Of $\tan ( u + v )$

Find the exact value of $\tan ( u + v )$ given that $\sin u = - \frac { 3 } { 5 }$ and $\cos v = \frac { 24 } { 25 }$ . (Both $u$ and $v$ are in Quadrant IV.)

A) $\tan ( u + v ) = \frac { 41 } { 75 }$
B) $\quad \tan ( u + v ) = \frac { 38 } { 75 }$
C) $\tan ( u + v ) = - \frac { 4 } { 3 }$
D) $\tan ( u + v ) = \frac { 89 } { 75 }$
E) $\tan ( u + v ) = - \frac { 39 } { 25 }$

Correct Answer:

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