I have spent about 2.5 hours on this question and I just can not seem to get anywhere. Please can someone show me how to do this.

Locate and classify the singularities (giving the order of any poles) of the functionMy attempts so far....

f(z) = z^3/(1-cos z)^2

Hint : Use cos z = cos (z - 2kpi ), for all K E Z

This function has singularities at 0, +/- 2pi, +/-4pi, +/-6pi; (As this is where denominator=0)

Also f is analytic on each punctured disc D= {z:0 < l z-2kpi l < 2pi}

I have seen a previous example, (z/sinz) whereby a hint of sin(z-kpi)=(-1)^ksin z was used and wondered if I had to apply a similar approach?

Please help as I am experiencing difficulties in using the Laurent's theorem?

Shoni