14 May
2011
14 May
'11
9:28 a.m.
You can usually lose all the trig functions with
cos u -> (1 - u^2)/(1 + u^2), sin u -> 2 u / (1 + u^2),
and similar for v. The new u has range [-1,1], assuming the original u was real. This is the ancient tan(u/2) -> u substitution.
Yes, I use that whenever I need to show that two trigonometric expressions are equal, as polynomial expressions are much easier to compare. Sincerely, Adam P. Goucher