Final answer:
To find cos(a-b) given tan a and cos b, we can use the formula cos(a-b) = cos(a)cos(b) + sin(a)sin(b). By substituting the given values of tan a and cos b into the formula, we can calculate the value of cos(a-b).
Step-by-step explanation:
To find cos(a-b), we can use the formula:
cos(a-b) = cos(a)cos(b) + sin(a)sin(b)
Given that tan a = 3/4 in the third quadrant and cos b = 4/5 in the first quadrant, we can determine the values of cos(a) and sin(a) using the Pythagorean identity. Since tan a = sin a / cos a, we have sin a = 3 and cos a = -4. Using these values, we can substitute them into the formula to find the value of cos(a-b).
cos(a-b) = (-4)(4/5) + (3)(3/5) = -16/5 + 9/5 = -7/5