ades CommunicationAssessments ToolsResources Module 2 Inver

ades CommunicationAssessments ToolsResources ) Module 2: Inverse Trigonometric Functions, Their Graphs, and Basic Equations Quiz and TestModule 2 eft:1:2707 Eric Santiago: Attempt 1 Question 15 (3 points) Show your work! Use of the Equation Editor is recommended Write the trigonometric expression as an algebraic expression in x. Assume x is positive. Rationalize the answer if necessary cos(cot 1 x Format

Solution

We are given Cos (Cot^-1 x) to be written in algebraic form.

Let Cot^-1 x =

=> Cot = x = x/1

Now from this and by the definition of Cot, we have base = x and perpendicular = 1,

So the hypotenuse by the Pythagorean theorem is : (1 + x²)

So, Cos (Cot^-1 x) = Cos() = base/hypotenuse

Cos (Cot^-1 x) = x / (1 + x²)

It is required algebraic expression.