Question 1055474
<pre>
{{{(tanA+cotB)/(tanB+cotA)}}}{{{""=""}}}{{{tanA*cotB}}}

We will use the fact that since tangent and cotangent are
reciprocals, that their product equals 1:

{{{tan(theta)cot(theta) = tan(theta)expr(1/tan(theta))=cross(tan(theta))expr(1/cross(tan(theta)))}}}{{{""=""}}}{{{1}}}

Indicate 1's multiplied by the terms on top:

{{{(tanA*1+cotB*1)/(tanB+cotA)}}}{{{""=""}}}

Substitute the products of a tangent by a cotangent
for the 1's: 

{{{(tanA*(tanB*cotB)+cotB*(tanA*cotA))/(tanB+cotA)}}}{{{""=""}}}

Erase the unnecessary parentheses: 

{{{(tanA*tanB*cotB+cotB*tanA*cotA)/(tanB+cotA)}}}{{{""=""}}}

Factor tanA*cotB out if the numerator:

{{{(tanA*cotB(tanB+cotA))/(tanB+cotA)}}}{{{""=""}}}

Cancel the tanB+cotA's

{{{(tanA*cotB(cross(tanB+cotA)))/(cross(tanB+cotA))}}}{{{""=""}}}

{{{tanA*cotB}}}

Edwin</pre>