Trigonometry: Using Double Angle Formula for Tangent to Prove an Equality

**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. :)