Final answer:
The trigonometric expression sec(cos⁻¹u) can be written as an algebraic expression in u as 1/u.
Step-by-step explanation:
To write the trigonometric expression as an algebraic expression in u, we need to express it in terms of sine and cosine. We can use the identity sec(x) = 1/cos(x) to rewrite sec(cos⁻¹u) as 1/cos(cos⁻¹u). Since cos(cos⁻¹u) = u (the cosine function and its inverse cancel each other out), the expression simplifies to 1/u.