Question

cos(2arctan x)

Answer 1

is the anwer 2/root x^2 + 4?

Answer 2

yikes. first you need
\[\cos(2\theta) = 2\cos^2(\theta)-1\] and then you need
\[\cos(\arctan(x))\]

Answer 3

can't i do arctan y =x/2?

Answer 4

first we find
\[\cos(\arctan(x))\] as before and see that it is
\[\frac{1}{\sqrt{1+x^2}}\]

Answer 5

(1-x^2)/(x^2+1)

Answer 6

yup

Answer 7

then square, double, and subtract 1 to get
\[\frac{2}{1+x^2}-1\]