Solve the expression sin pi/6 - cos pi/3 .

First, we'll notice that we'll have to calculate the difference of 2 complementary functions of 2 complementary angles.

We know that sin pi/6 = cos (pi/2 - pi/6) = cos (2pi/6) = cos pi/3

We'll substitute in the given expression sin pi/6 by cos pi/3 and we'll get:

 cos pi/3 - cos pi/3 = 0

Note: Also, we could substitute the functions by their values, knowing that

sin pi/6=1/2 and cos pi/3=1/2

sin pi/6 - cos pi/3  = 1/2 - 1/2 = 0