Final answer:
To find tan(a - b), use the trigonometric identity tan(a - b) = (tan(a) - tan(b))/(1 + tan(a)tan(b)). Substituting the given values for tan(a) and tan(b), simplify the expression to find the value of tan(a - b). The value of tan(a - b) is -96/281.
Step-by-step explanation:
To find tan(a - b), we can use the trigonometric identity tan(a - b) = (tan(a) - tan(b))/(1 + tan(a)tan(b)). Given that tan(a) = 8/15 and tan(b) = 20/21, we can substitute these values into the formula to find the value of tan(a - b).
Using the given values, we have tan(a - b) = (8/15 - 20/21)/(1 + (8/15)(20/21)).
Simplifying this expression, we get, tan(a - b) = (-32/105)/(281/315).
Further simplifying, we get tan(a - b) = -96/281. Therefore, tan(a - b) = -96/281.