Hi Ali812, welcome to MHF.
2arctan(1/5) = arctan[2/5/(1-1/25) = arctan(10/24) = arctan(5/12)
Similarly
2arctan(5/12) = ...........?
1. The problem statement, all variables and given/known data
Show that is equivalent to
2. Relevant equations
Double Angle Formula for tan:
3. The attempt at a solution
From my understanding you have to apply the double angle formula twice.
Set x = arctan(1/5) and plug that into the double angle formula to solve for tan(2arctan1/5) (which is basically 2x). Now I set 2x = y, and plug y into the double angle formula to solve for 2y, which is 4arctan1/5.
sub x = arctan(1/5) into the double angle formula:
Apply tan(arctanx) = x into the formula, resulting with:
Simplify the numerator:
At this point I'm stuck, did I mess up in simplifying the denominator because I would like to be able to simplify it further so I don't have to use the final result above when I plug it back into a double angle formula once more. If that is correct, how would I work solve for
?
Thanks for any assistance.