To simplify the expression (1 + cos a)/(sin^2(a/2)), we can start by using the double angle identity for sine: sin(2x) = 2sin(x)cos(x). We can rewrite sin^2(a/2) as sin(a/2)sin(a/2) = (1 - cos(a))/2.

Now the expression becomes (1 + cos a)/((1 - cos a)/2) = 2(1 + cos a)/(1 - cos a).

Next, we can use the difference of squares formula to factor the denominator:

2(1 + cos a)/(1 - cos a) = 2(1 + cos a)/((1 - cos a)(1 + cos a)).

Finally, we can cancel out the common factors of (1 + cos a) in the numerator and the denominator:

2/(1 - cos a).

Therefore, the simplified expression is 2/(1 - cos a).