Answer:
-13/84
Step-by-step explanation:
Calculation to Find the exact value of the trigonometric expression
First step is to find tan(u)
Based on the information given we were told that sin(u) = -3/5 which means if will have -3/5 in the 4th quadrant would have triangle 3-4-5
Hence:
tan(u)=-3/4
Second step is to calculate tan(v)
In a situation where cos(v) is 15/17 which means that we would have triangle 8-15-17
Hence:
tan(v) = 8/15
Now Find the exact value of the trigonometric expression using this formula
tan(u+v) = (tan(u) + tan(v))/(1-tan(u)tan(v)
Where,
tan(u)=-3/4
tan(v)=8/15
Let plug in the formula
tan(u+v)=(-3/4)+(8/15)÷[1-(-3/4)(8/15]
tan(u+v)=(-45+32)÷(60-24)
tan(u+v)=-13/84
Therefore exact value of the trigonometric expression will be -13/84
