The expression can be simplified using the trigonometric identity:sin(a)cos(b) - cos(a)sin(b) = sin(a-b).
Therefore, sin(π/8)cos(3π/8) - cos(π/8)sin(3π/8) = sin(π/8 - 3π/8) = sin(-π/4) = -√2/2.
So, the simplified expression is -√2/2.
The expression can be simplified using the trigonometric identity:
sin(a)cos(b) - cos(a)sin(b) = sin(a-b).
Therefore, sin(π/8)cos(3π/8) - cos(π/8)sin(3π/8) = sin(π/8 - 3π/8) = sin(-π/4) = -√2/2.
So, the simplified expression is -√2/2.