Use trig identities to show that

[ivan_x3000]

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

 

[jbunniii]

Maybe try bringing $\sin(\tan^{-1}(x))$ into the picture?

 

[Dick]

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

tan^(-1)(x) represents an angle whose opposite side is x and whose adjacent side is 1. Use that geometry to figure out the cosine.

 

[SammyS]

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

cos → sec → tan