SOLUTION: Rewrite (2tan 23°) / (1 - tan223° ) as a single function of an angle. See

Algebra ->  Trigonometry-basics -> SOLUTION: Rewrite (2tan 23°) / (1 - tan223° ) as a single function of an angle. See       Log On


   

Question 1205943: Rewrite (2tan 23°) / (1 - tan223° ) as a single function of an angle. See

Answer by ikleyn(53937) About Me  (Show Source):
You can put this solution on YOUR website!
.
Rewrite (2tan(23°)) / (1 - tan^2(23°)) as a single function of an angle.
~~~~~~~~~~~~~~~~~~~~ 

What is written in the post, is  (2tan(23°)) / (1 - tan^2(23°)),  or  %282tan%2823%5Eo%29%29+%2F+%281+-+tan%5E2%2823%5Eo%29%29.

Use the formula/identity  tan(2a) = %282%2Atan%28a%29%29%2F%281-tan%5E2%28a%29%29.


In your case, angle "a" is  a = 23°.  So, according to the formula,

    %282tan%2823%5Eo%29%29+%2F+%281+-+tan%5E2%2823%5Eo%29%29 = tan(2*23°) = tan(46°).


It is what you want to get.


ANSWER.  (2tan(23°)) / (1 - tan^2(23°)) = tan(46°).

Solved.