Question

Write as an algebraic expression in x free of trigonometric or inverse trigonometric functions:
cos(cot^-1x)

Answer 1

1/Sqrt[1 + 1/x^2]

Answer 2

So the answer should be:

\[\cos (\cot ^{-1}x)= \frac{ x }{ \sqrt{x ^{2}+1} }\]