You can solve the expression using trigonometric identities, specifically the sum of angles formula for sine.
sin(10°)cos(80°) + cos(10°)sin(80°)
= sin(10° + 80°) (Using the sum of angles formula for sine)
= sin(90°) (10° + 80° is equal to 90°)
= 1
So, sin(10°)cos(80°) + cos(10°)sin(80°) equals 1.