Final answer:
The expression simplifies to sin 120 degrees using the sine difference identity, yielding an exact value of √3/2 since 120 degrees is related to a 60 degrees reference angle.
Step-by-step explanation:
The expression sin 200 degrees * cos 80 degrees - cos 200 degrees sin 80 degrees is recognizable as a form of the sine difference identity, which is sin(α - β) = sinα cosβ - cosα sinβ. Using this identity with α = 200 degrees and β = 80 degrees gives us sin(200 - 80), which simplifies to sin 120 degrees.
The exact value of sin 120 degrees is √3/2 because 120 degrees is in the second quadrant where sine is positive and corresponds to a 60 degrees reference angle in a right triangle.