To find the value of the expression sin3x + sin5x / 2sin4x at x = π/8, we first need to substitute π/8 for x in the expression.

sin(3(π/8)) + sin(5(π/8)) / 2sin(4(π/8))

= sin(3π/8) + sin(5π/8) / 2sin(π/2)

= sin(3π/8) + sin(5π/8) / 2

Next, we need to find the values of sin(3π/8) and sin(5π/8) using trigonometric identities.

sin(3π/8) = sin(π/8 + π/4) = sin(π/8)cos(π/4) + cos(π/8)sin(π/4)

sin(5π/8) = sin(π/8 + π/2) = sin(π/8)cos(π/2) + cos(π/8)sin(π/2)

Now that we have found the values, we can substitute them back into the expression:

(sin(π/8)cos(π/4) + cos(π/8)sin(π/4) + sin(π/8)cos(π/2) + cos(π/8)sin(π/2)) / 2

Finally, evaluate this expression to find the numerical value at x = π/8.