To prove that sin(60°)cos(60°) - sin(30°)cos(60°) = sin(30°), we can use the trigonometric identity sin(A - B) = sin(A)cos(B) - cos(A)sin(B).
Let A = 60° and B = 30°.
Using the trigonometric identity, sin(60° - 30°) = sin(60°)cos(30°) - cos(60°)sin(30°).
Simplifying, sin(30°) = sin(60°)cos(30°) - cos(60°)sin(30°).
Rearranging the terms on the right side, we get:
sin(30°) + cos(60°)sin(30°) = sin(60°)cos(30°).
Combining like terms on the left side, we obtain:
(1 + cos(60°))sin(30°) = sin(60°)cos(30°).
Using the value of cos(60°) = 1/2 and sin(30°) = 1/2, we can substitute these values in:
(1 + 1/2)(1/2) = (1/2)(1/2).
(3/2)(1/2) = 1/4.
3/4 = 1/4.
Therefore, sin(60°)cos(60°) - sin(30°)cos(60°) = sin(30°).