let sinA=5/13 ,cosA>0 and tanB=4/3 cosB=0 find the exact value of cos(A-B).
This is wrong where it says cosB = 0, so that part is being ignored (not needed anyway).
sinA = 5/13.
Therefore cosA = 12/13 (use a right-angled triangle and pythagoras' theorem)
tanB = 4/3,
Therefore, cosB = 3/5, sinB = 4/5 (again, use right-angled triangle)
cos(A + B) = cosA.cosB + sinA.sinB = (12/13)(3/5) + (5/13)(4/5) = 36/65 + 4/13 = 56/65
Answer: cos(A - B) = 56/65