Trigonometry help?

Let arcsin(x) = A
Then sin(A) = x
and cos(A) = ±√[1 - sin²(A)] = ±√(1 - x²)

Let arccos(x) = B
Then cos(B) = x
and sin(B) = ±√[1 - cos²(B)] = ±√(1 - x²)

sin[arcsin(x) - arccos(x)]
= sin(A - B)
= sin(A) cos(B) - cos(A) sin(B)
= x • x - [±√(1 - x²)] • [±√(1 - x²)]
= x² - [±√(1 - x²)]²
= x² - (1 - x²)
= x² - 1 + x²
= 2x² - 1

use sin ( a - b ) = sin a cos b - cos a sin b....sin a = x ---> cos a = √(1 - x²) , etc