Answer: -sqrt(3)/4
Explanation:
To solve this trigonometric expression, we can use the following trigonometric identities:
sin (180 + x) = -sin x
cos (180 + x) = -cos x
Using these identities, we can rewrite the expression as:
sin(200°)cos(80°) - cos(200°)sin(80°)
= sin(180° + 20°)cos(80°) - cos(180° + 20°)sin(80°)
= -sin(20°)cos(80°) + cos(20°)sin(80°)
= (cos(20°) - sin(20°))sin(80°)
= sin(70°)sin(80°)
= (cos(20°) - cos(150°))/2
= (-sqrt(3)/2 - sqrt(3)/2)/2
= -sqrt(3)/4
Therefore, sin(200°)cos(80°) - cos(200°)sin(80°) = -sqrt(3)/4.