Question

How to solve

arctan(2x)+arctan(x)=pi/4

Answer 1

You could try to use the formula:\[\tan (a+b)=\frac{ \tan a + \tan b }{ 1-\tan a \tan b}\]

Answer 2

Apply tan on both sides:
\[\tan(\arctan 2x + \arctan x)=\tan \frac{ \pi }{ 4 }=1\]Now use the sum formula above:\[\frac{ \tan(\arctan 2x)+\tan(\arctan x) }{ 1-\tan(\arctan2x)\tan(\arctan x) }=\frac{ 2x+x }{ 1-2x*x }=\frac{ 3x }{ 1-2x^2 }=1\]All you have to do now is solve this one!

Answer 3

Please give it a try...