The domain of the function given are:
y=cot x
{x∈R: πn<x<π(n+1)} where n any integer
y=csc x
{x∈R: πn<x<π(n+1)} where n any integer
y=cos x
R (all real numbers)
y=sec x
{x∈R:π(n+1/2)<x<π(n+3/2)} where n is all integers.
from above we see that the the function that has a domain of all real numbers except npi is y=cot x and y=csc x
