Simplify the expression: sin(pi/6 + t)cos(pi/3 - t) + sin(pi/3 + t)sin(pi/6 - t)

The expression is in the form sin(A)cos(B) + cos(A)sin(B) where A = pi/6 + t and B = pi/3 - t. This simplifies to sin(A+B).

A + B = (pi/6 + t) + (pi/3 - t) = pi/6 + pi/3 = pi/2.

Therefore, the expression simplifies to sin(pi/2) = 1.