Rewrite secsin−1u5 as an algebraic expression in u.=secsin−1u5

The given expression is sec(sin^-1(u/5)).

Step 1: Let's denote sin^-1(u/5) as θ. So, θ = sin^-1(u/5).

Step 2: From the definition of sin, we know that sin θ = u/5.

Step 3: We can form a right triangle with opposite side as 'u' and hypotenuse as '5'. The adjacent side can be found using Pythagorean theorem, which is sqrt(5^2 - u^2) = sqrt(25 - u^2).

Step 4: The secant of an angle in a right triangle is the ratio of the hypotenuse to the adjacent side. So, sec θ = 5/sqrt(25 - u^2).

Step 5: Substituting θ back into the expression, we get sec(sin^-1(u/5)) = 5/sqrt(25 - u^2).

So, the algebraic expression of sec(sin^-1(u/5)) in terms of 'u' is 5/sqrt(25 - u^2).