How do you evaluate $tan(4(tan^-1(1/5))$ ?

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Answer 1 · 2016-07-02T13:25:32

$120/119$

Let $a = tan(-1)(1/5)$ . Then $tan a = 1/5$ .

$tan 2a = (2tana)/(1-tan^2 a)=(2(1/5))/(1-1/25)=5/12$

Likewise, the given expression $tan 4a = (2 tan 2a)/(1-tan^2(2a))$

$=(2(5/12))/(1-(5/12)^2)$

$=120/119$ .

How do you evaluate tan(4(tan^-1(1/5))tan(4(tan^-1(1/5))?