Rewrite secsin−13u as an algebraic expression in u.

The given expression is sec(sin^(-1)(3u)).

Step 1: Let's denote sin^(-1)(3u) as x for simplicity. So, x = sin^(-1)(3u).

Step 2: From the definition of inverse sine, we know that sin(x) = 3u.

Step 3: We can form a right triangle with this information. The opposite side (in relation to angle x) is 3u and the hypotenuse is 1. Using the Pythagorean theorem, the adjacent side is sqrt(1 - (3u)^2).

Step 4: The secant of an angle in a right triangle is the ratio of the hypotenuse to the adjacent side. So, sec(x) = 1/sqrt(1 - (3u)^2).

Step 5: Substituting x back in, we get sec(sin^(-1)(3u)) = 1/sqrt(1 - (3u)^2).

So, the algebraic expression of sec(sin^(-1)(3u)) in terms of u is 1/sqrt(1 - (3u)^2).