To prove this equality, we will simplify the left side of the equation using trigonometric identities.

Given:
cos(x) / (3sin(x)) = 1/ctg(x)

First, we know that cotangent is the reciprocal of tangent, so ctg(x) = 1/tan(x).

Now, we simplify the left side of the equation:
cos(x) / (3sin(x)) = cos(x) / (3sin(x))
= cos(x) / (3 sin(x))
= cos(x) / (3 sin(x))
= cos(x) / (3 sin(x))
= cos(x) / 3 sin(x)
= 1/3 * cot(x)

Now, we have:
1/3 * cot(x) = 1/ctg(x)

Therefore, cos(x) / (3sin(x)) = 1/ctg(x) is proven to be true.