Rewrite sin (pi over 4 - pi over 6) using a compound angle formula. Then calculate the exact value of the expression.
To rewrite sin(pi/4 - pi/6) using a compound angle formula, we can use the formula sin(A - B) = sin A cos B - cos A sin B.
In this case, A = pi/4 and B = pi/6.
So, sin(pi/4 - pi/6) = sin(pi/4)cos(pi/6) - cos(pi/4)sin(pi/6).
Now, we can calculate the values:
sin(pi/4) = 1/sqrt(2)
cos(pi/6) = sqrt(3)/2
cos(pi/4) = 1/sqrt(2)
sin(pi/6) = 1/2
Substituting these values into the expression:
sin(pi/4 - pi/6) = (1/sqrt(2))(sqrt(3)/2) - (1/sqrt(2))(1/2)
= sqrt(3)/(2sqrt(2)) - 1/(2sqrt(2))
= (sqrt(3) - 1)/(2sqrt(2))
Therefore, the exact value of sin(pi/4 - pi/6) is (sqrt(3) - 1)/(2sqrt(2)).