Evaluate Trig functions

[Tinkermom]

Evaluate

tan(2tan^-1 2)

I missed a day in school, and am lost on inverse functions. Is tan^-1 of 2 still 2? If so, then would it be 2 x 2? Then would that be tan of 4?

 

[DrSteve]

You need to use the double angle formula \(\displaystyle \tan 2A=\frac{2\tan A}{1-\tan^2 A}\) to get

\(\displaystyle \frac{2tan(tan^{-1}2)}{1-tan^2(tan^{-1}2)} = \frac{2*2}{1-2^2} = -\frac{4}{3}\).

 

[Deleted member 4993]

Evaluate

tan(2tan^-1 2)

I missed a day in school, and am lost on inverse functions. Is tan^-1 of 2 still 2? If so, then would it be 2 x 2? Then would that be tan of 4?

Let:

\(\displaystyle tan^{-1}(2) \ = \ \theta\)

then

\(\displaystyle tan(\theta) \ = \ 2\) ...........................(1)

Then your problem becomes:

\(\displaystyle tan(2\theta)\)

Now express tan(2?) in terms of tan(?) - then use (1) to evaluate tan(2?)

 

[Tinkermom]

Oh...ok, I see it now.

Thank you very much.