To prove the equation sin(5x)cos(x) - cos(5x)sin(x) = 1, we will use the angle addition formula for sine and cosine:

sin(a + b) = sin(a)cos(b) + cos(a)sin(b)
cos(a + b) = cos(a)cos(b) - sin(a)sin(b)

Using these formulas, let's simplify sin(5x)cos(x) - cos(5x)sin(x):

sin(5x)cos(x) - cos(5x)sin(x)
= sin(5x + x) (using sin(a + b) = sin(a)cos(b) + cos(a)sin(b))
= sin(6x)
= 1(sin(6x))1
= 1

Therefore, sin(5x)cos(x) - cos(5x)sin(x) = 1.