Question 969275
<pre>
{{{tan(2x)cot(x)}}}{{{""=""}}}{{{cot(2x)tan(x)}}}

We must rule out all values where some of those are undefined,

{{{x<>n*pi/4}}}, or all multiples of 45°

{{{tan(2x)/tan(x)}}}{{{""=""}}}{{{tan(x)/tan(2x)}}}

{{{tan^2(2x)}}}{{{"=""}}}{{{tan^2(x)}}}

{{{tan(2x)}}}{{{""=""}}}{{{"" +- tan(x)}}}

{{{(2tan(x))/(1-tan^2(x))}}}{{{""=""}}}{{{"" +- tan(x)}}}

{{{2tan(x)}}}{{{""=""}}}{{{"" +- tan(x)(1-tan^2(x)^"")}}}

We can divide both sides by tan(x) since tan(x) cannot be 0.

{{{2}}}{{{""=""}}}{{{"" +- (1-tan^2(x)^"")}}}

Using the + sign,

{{{2}}}{{{""=""}}}{{{""+(1-tan^2(x)^"")}}}
{{{2}}}{{{""=""}}}{{{1-tan^2(x)}}}
{{{tan^2(x)}}}{{{""=""}}}{{{-1}}}

This would give an imaginary answer.

Using the - sign,

{{{2}}}{{{""=""}}}{{{-(1-tan^2(x)^"")}}}
{{{2}}}{{{""=""}}}{{{-1+tan^2(x)}}}
{{{3}}}{{{""=""}}}{{{tan^2(x)}}}
{{{"" +- sqrt(3)}}}{{{""=""}}}{{{tan(x)}}}

{{{x}}}{{{""=""}}}{{{pi/3+n*pi}}},{{{2pi/3+n*pi}}}
{{{x}}}{{{""=""}}}{{{expr(pi/3)(1+3n)}}},{{{expr(pi/3)(2+3n)}}}

or in degrees:

{{{x}}}{{{""=""}}}{{{"60°"+"180°"n}}}, {{{"120°"+"180°"n}}}
{{{x}}}{{{""=""}}}{{{"60°"(1+3n)}}}, {{{"60°"(2+3n)}}}

Edwin</pre>