Cos (tan-1 x)
`cos(tan^-1 x) = 1/sqrt(1+x^2)`
If you need to prove the identity, then here are the steps.
First we will assume that arctanx = A
==> tanA = x
But we know that tanA = `sinA/cosA ` = opposite side/adjacent side= `x/1` Then we can assume that we have aright angle triangle such that the sides are x and 1.
Then, the hypotenuse is `h= sqrt(1^2+x^2)= sqrt(1+x^2).`
Now we need to find `cos(tan^-1x)`
`cos(tan^-1 x) = cos(A) =(adjacent)/h = 1/sqrt(1+x^2)` ==> `cos(tan^-1 x) = 1/sqrt(1+x^2)`