SOLUTION: If tan theta=8, find the exact value of cot(pi/2-theta).

 so we draw a very steep
right triangle with the opposite = 8 and the adjacent = 1. 



The small sharp angle at the top is the complement of q


So 

"COtangent" is an abbreviation for "COmplement's tangent",
and cot(p/2-q) IS q's COmplement's tangent. 
That's why both are equal.

The opposite side of q is the adjacent side of p/2-q and vice-versa.

Edwin