The discussion focuses on proving the trigonometric identity cos(tan^(-1)(x)) = 1/√(1+x^2) for the interval −π/2 < x < π/2. Participants emphasize the application of Pythagorean identities and geometric reasoning, specifically using the right triangle definition of the tangent function. By considering tan^(-1)(x) as an angle with an opposite side of x and an adjacent side of 1, the cosine can be derived using the relationship between the sides of the triangle.
PREREQUISITESStudents studying trigonometry, mathematics educators, and anyone looking to deepen their understanding of trigonometric identities and their applications in geometry.
ivan_x3000 said:Homework Statement
use trig identities to show that
(b) cos(tan^(−1)[x])=1/√(1+x^2) for −1/2π<x<1/2π.
Homework Equations
i think Pythagoras has to applied but that is geometric reasoning hmm
The Attempt at a Solution
ivan_x3000 said:Homework Statement
use trig identities to show that
(b) cos(tan^(−1)[x])=1/√(1+x^2) for −1/2π<x<1/2π.
Homework Equations
i think Pythagoras has to applied but that is geometric reasoning hmm
The Attempt at a Solution