How do you prove the identity #tan2XcotX=3#?

1 Answer
Oct 7, 2015

It isn't.

Explanation:

#tan(2x)*cot(x) = 3#

Using the double angle formula,

#(2tan(x))/(1-tan^2(x))*cot(x) = 3#

Knowing that #tan(x)*cot(x) = 1#

#2/(1-tan^2(x)) = 3#

Which is obviously false, as the tangent range from #-oo# to #oo#.
If you continue to work this like it was an equation, you'll see this only has two tangent values for solutions, #+-sqrt(3)/3#.