What is cos(arctan(x)) ?

The solution to cos(arctan(x)) is (sqrt(1+x^2))/(1+x^2)

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simplify cos(arctan(x))

simplify

cos (arctan (x))

\frac{1 + x ^{2}}{1 + x ^{2}}

Solution steps

cos (arctan (x))

Use the following identity:

cos (arctan (x)) = \frac{1 + x ^{2}}{1 + x ^{2}}

= \frac{1 + x ^{2}}{1 + x ^{2}}

What is cos(arctan(x)) ?
The solution to cos(arctan(x)) is (sqrt(1+x^2))/(1+x^2)