Question 1056804
<pre><b>
{{{cot^""(A)}}}{{{""-""}}}{{{tan^""(A)}}}{{{""=""}}}{{{2cot^""(2A)}}}

Work with the right side:

{{{2cot^""(2A)}}}

{{{2^""/tan^""(2A)}}}

{{{2}}}{{{"÷"}}}{{{tan^""(2A)}}}

Use formula for tan(2A)

{{{2}}}{{{"÷"}}}{{{((2tan^""(A))/(1-tan^2(A)))}}}

Invert the second and multiply:

{{{2}}}{{{"×"}}}{{{((1-tan^2(A))/2tan^""(A)))}}}

{{{cross(2)}}}{{{"×"}}}{{{((1-tan^2(A))/cross(2)tan^""(A)))}}}

{{{(1-tan^2(A))/tan^""(A))}}}

Break into two fractions:

{{{1^""/tan^""(A)}}}{{{""-""}}}{{{tan^2(A)/tan^""(A)}}}

{{{cot^""(A)}}}{{{""-""}}}{{{tan^cross(2)(A)/cross(tan^""(A))}}}

{{{cot^""(A)}}}{{{""-""}}}{{{tan^""(A)}}}

Edwin</pre></b>