Question

Write each expression as an algebraic​ (nontrigonometric) expression in​ u, u > 0.

sin(2sec^-1 u/10)

Answer 1

Explanation:

We want to write the trignometric expression:

As an algebraic equation.

First, we can focus on the inner expression. Let θ equal the expression:

Take the secant of both sides:

Since secant is the ratio of the hypotenuse side to the adjacent side, this means that the opposite side is:

By substitutition:

Using an double-angle identity:

We know that the opposite side is √(u² -100), the adjacent side is 10, and the hypotenuse is u. Therefore:

Simplify. Therefore: