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

1 Answer
Oct 7, 2015

It isn't.

Explanation:

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

Using the double angle formula,

(2tan(x))/(1-tan^2(x))*cot(x) = 32tan(x)1tan2(x)cot(x)=3

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

2/(1-tan^2(x)) = 321tan2(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±33.