Final answer:
To find cos(A-B), we can use the trigonometric identity cos(A-B) = cosA * cosB + sinA * sinB. First, find cosA and sinB using their respective trigonometric identities. Then, substitute these values into the formula to get the answer.
Step-by-step explanation:
To find cos(A-B), we can use the trigonometric identity cos(A-B) = cosA * cosB + sinA * sinB. First, we need to find sinB and cosA.
Given that sinA = 4/5, we can use the Pythagorean identity sin^2A + cos^2A = 1 to find cosA. Plugging in the value of sinA, we get cosA = -3/5.
Given that cosB = -5/13, we can use the Pythagorean identity sin^2B + cos^2B = 1 to find sinB. Plugging in the value of cosB, we get sinB = 12/13.
Now we can substitute these values into the formula cos(A-B) = cosA * cosB + sinA * sinB to find the answer.
cos(A-B) = (-3/5)(-5/13) + (4/5)(12/13) = 15/65 + 48/65 = 63/65.