Final answer:
The coefficient of z^-2 in the Laurent series expansion of (1)/(1-cos(z)) around z=0 is -1/2.
Step-by-step explanation:
To find the Laurent series expansion of the function (1)/(1-cos(z)) around z=0, we can use the Maclaurin series expansion of cos(z). The Maclaurin series expansion of cos(z) is 1 - (1/2)z^2 + (1/24)z^4 - ...
Substituting this into the given expression, we get (1)/(1 - (1/2)z^2 + (1/24)z^4 - ...).
To find the coefficient of z^-2, we need to find the term with z^-2 in the expansion. This term is obtained by multiplying the coefficient of z^2 in the denominator (which is (-1/2)) by the coefficient of z^2 in the numerator (which is 1). Therefore, the coefficient of z^-2 is (-1/2) * 1 = -1/2.