How do you simplify $tan (2 arctan x)$ $tan(2 arctan x)$ ?

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Answer 1 · 2016-10-31T13:23:23

tan (2x)

arctanx --> x
tan (2arctan x) --> tan (2x)

Answer 2 · 2016-10-31T18:18:53

$tan (2 arctan x) = \frac{2 x}{1 - x^{2}}$ $tan(2arctanx)=(2x)/(1-x^2)$

Let $arctan x = θ$ $arctanx=theta$ , then

$x = tan θ$ $x=tantheta$

$tan (2 arctan x) = tan 2 θ$ $tan(2arctanx)=tan2theta$

= $\frac{2 tan θ}{1 - {tan}^{2} θ}$ $(2tantheta)/(1-tan^2theta)$

= $\frac{2 x}{1 - x^{2}}$ $(2x)/(1-x^2)$

How do you simplify tan(2arctanx)tan(2 arctan x)?