The value of cos(2a + b) can be found by using the double angle formula, which states that cos(2a + b) = 2cos^2(a) - 1 + 2cos(a)sin(b). Substituting a = sin^(-1)(4/5) and b = tan^(-1)(12/5) gives us cos(2a + b) = 2(4/5)^2 - 1 + 2(4/5)sin(tan^(-1)(12/5)) = 14/25.