Given that tan(a) = 1/3, we can use the Pythagorean identity to find cos(a):

cos^2(a) = 1 / (1 + tan^2(a))
cos^2(a) = 1 / (1 + (1/3)^2)
cos^2(a) = 1 / (1 + 1/9)
cos^2(a) = 9 / 10

Now we can substitute cos^2(a) into the original expression:

2cos^2(a) + 1
2(9/10) + 1
18/10 + 10/10
28/10
2.8

Therefore, the value of the expression 2cos^2(a) + 1 when tan(a) = 1/3 is 2.8.