Angle sum and difference

Question

For positive acute angles A and B, it is known that sin A= 3/5 and tan B= 5/12. Find the value of cos (A - B) in the simplest form.

Please help, it's due at 4pm

Answer 1

sinA = 3/5 A=36.9

cosA = 4/5

tanB =5/12 B=22.6

sinB = .38,

cosB=.91.9

A-B = 36.9-22.6 = 14.3

cos(A-B) = cos(14.3) = .97

cos(A-B)= cosAcosB + sinAsinB = (4/5)(.91)+3/5(.38) = .73+.23 = .96

it's possible there's a misprint in the problem and tanB should have been 5/13. that's a common right triangle

so that sinB = 5/13 and cosB =12/13

then cos(A-B) = (4/5)(12/13) + (3/5)(5/13) = (48+15)/65 = 63/65 = about .97

the answer is basically the same, however the exact answer is far more simple