Question

hey guys, need help is solving cos(2tan^-1x)

Answer 1

what do you have to do with that function...

Answer 2

simplify probably :)

Answer 3

yea fair call, probs a good idea to apply what arctanx means

Answer 4

\[\large\rm \cos(2\color{orangered}{\arctan x})\]

If \(\large\rm arctan x=\theta\) then \(\large\rm \tan\theta=x\)
This arctangent is just some angle.\[\large\rm \cos(2\color{orangered}{\arctan x})=\cos(2\color{orangered}{\theta})\]So we need to apply our Double Angle Formula for Cosine.
It shows up in three different forms, any of them will do.\[\large\rm \cos(2\theta)=2\cos^2\theta-1\]

Answer 5

We should draw a triangle to show what is going on with this tangent function.

Answer 6

\[\large\rm \tan \theta=x\qquad\to\qquad \tan\theta=\frac{x}{1}=\frac{opposite}{adjacent}\]