What algebraic expression is equivalent to the expression cos(arcsin((a-x)/c))?

Let arcsin(a-x)/c = y, therefore sin [arcsin(a-x)/c] = sin
y = (a-x)/c

Using Pythagorean identity, we'll get cos
t:

cos y = sqrt[1 - (sin
y)^2]

cos y = sqrt[1 -
(a-x)^2/c^2]

cos y = sqrt {[c^2 -
(a-x)^2]/c^2}

The difference of sqares returns the
product:

cos y = sqrt [(c - a + x)(c + a -
x)/c^2]

cos y = [sqrt (c - a + x)(c + a -
x)]/c

The algebraic expression equivalent to
cos[arcsin(a-x)/c] is [sqrt (c - a + x)(c + a -
x)]/c.