Question

http://webwork.math.ttu.edu/wwtmp/equations/60/d9b2cde685d4c765be6c882b7c87f71.png

How do I evaluate this statement?

Answer 1

what is
\[ tan(2tan^{-1}(x)) \]
to answer this you need to know 3 things:

\[ tan(2a) = \frac{2 tan(a)}{1-tan^{2}(a)} \]
tan(a) = some number. call it x:
tan(a)= x
so
\[ a= tan^{-1}(x) \]

using this we replace inverse tan with the angle a:
\[ tan(2tan^{-1}(x))= tan(2a) \]
now rewrite to get rid of the double angle 2a:
\[ tan(2a) = \frac{2 tan(a)}{1-tan^{2}(a)} \]
now use tan(a)= x
to get
\[\frac{2 x}{1-x^{2}} \]