Trigonometric reduction formulas

[Nigel (UK)]

If you ask the Prime to simplify \[\tan\left({\pi\over 2}-x\right)-{1\over \tan(x)}\] it returns zero, so it knows that the two expressions are equal. However, it won't simplify either one to the other. A possible reason is that it has no way of knowing which form you consider to be simpler.

If I ask the Prime to expand \(\tan(a+b)\) with the texpand command, it does so. However, if \(a=\pi/2\) it returns undef. I guess that this is because \(\tan(\pi/2)\) is indeed undefined, although the Prime does correctly return \[\lim_{a\to\pi/2}
\Bigl({\rm texpand\,}\left(\tan\left(a-x\right)\right)\Bigr)\] as \(\cos(x)/\sin(x)\). Maybe the CAS could be given a new rule to allow it to expand \(\tan(a+b)\) when either \(a\) or \(b\) is an odd half-multiple of \(\pi\)?

Nigel (UK)