Question

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

Answer 1

`120/119`

Explanation:

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`.