Question 906268
<pre>
2sec(2a) = tan(b) + cot(b)

{{{2sec(2a)=sin(b)/cos(b)+cos(b)/sin(b)}}}

{{{2sec(2a)=(sin^2(b)+cos^2(b))/(cos(b)sin(b))}}}

{{{2sec(2a)=1/(cos(b)sin(b))}}}

Divide both sides by 2

{{{sec(2a)=1/(2cos(b)sin(b))}}}

{{{sec(2a)=1/(sin(2b))}}}

{{{1/cos(2a)=1/(sin(2b))}}}

{{{cos(2a)=sin(2b)}}}

Since we are looking for small positive values
of a and b, and since the sine of one equals 
the cosine of the other, we can take 2a and 2b 
as the acute angles of a right triangle. 

So 

2a+2b = 90°

Dividing thru by 2:

a+b = 45°

Edwin</pre>