- #1
tamtam402
- 201
- 0
Homework Statement
Let's say I'm asked to find the taylor expansion for cot x, at the given point a = π/2.
Homework Equations
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?