Given x = sqrt((a)/(b)), find x in terms of a and b.

We are given $\cos x = \sqrt{\frac{a}{b}}$.
The Pythagorean identity is $\sin^2 x + \cos^2 x = 1$.
Substitute the given value of $\cos x$:

$$\sin^2 x + \left(\sqrt{\frac{a}{b}}\right)^2 = 1$$ $$\sin^2 x + \frac{a}{b} = 1$$

Subtract $\frac{a}{b}$ from both sides:

$$\sin^2 x = 1 - \frac{a}{b}$$

Combine the terms on the right side:

$$\sin^2 x = \frac{b}{b} - \frac{a}{b}$$ $$\sin^2 x = \frac{b-a}{b}$$

Take the square root of both sides:

$$\sin x = \pm\sqrt{\frac{b-a}{b}}$$

The cosecant function is the reciprocal of the sine function:

$$\csc x = \frac{1}{\sin x}$$

Substitute the expression for $\sin x$:

$$\csc x = \frac{1}{\pm\sqrt{\frac{b-a}{b}}}$$

To simplify, we can flip the fraction inside the square root:

$$\csc x = \pm\sqrt{\frac{b}{b-a}}$$

The value of $\csc x$ is $\boxed{\pm\sqrt{\frac{b}{b-a}}}$.