what is the answer

Question

For positive acute angles A and B, it is known that cos⁡A=60/61 and tan⁡B=12/35.  Find the value of cos⁡(A−B) in simplest form.

Answer 1

cosA=60/61

sinA = 11/61

A = about 10.39 degrees

tanB = 15/35 = 3/7

B = about 23.2 degrees

cosA-B =cos(10.39-23.2) = cos(-12.81) =about 0.975

sinB =15/38.1

cosB =35/38.1

cos(A-B) = cosAcosB+sinAsinB = (60/61)(35/38.1)+(11/61)(15/38.1) = ((60)(35)+ (11)(15))/(61)(38.1)= 2265/2324.1 = about 0.975