1. The problem statement, all variables and given/known data Let's say I'm asked to find the taylor expansion for cot x, at the given point a = π/2. 2. Relevant equations 3. The attempt at a solution My first thought would be to take the mc laurin series expansion for cotx, which is: cot x = 1/x + x/3 - x3/45 ... and substitute x for z-π/2. According to my solution manual, that isn't correct. By messing around with trig identities, I solved the problem in the following way: cot x = cot (π/2 + x - π/2) = -tan(x - π/2) I took the mc laurin series expansion for tanx, multiplied it by -1, replaced x by z-π/2 and found the right answer. Why wasn't I allowed to substitute x = z - π/2 in cot x, yet doing the same thing in -tanx gave me the right answer?