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**why is cot(x) continious in (0,pi) ???**

why is cot(x) continious in (0,pi) ???

I mean Cot(x)=1/Tan(x) , now at pi/2 , tan(x) tends to infinity => 1/tan(x) tends to 0 , now

1/tan(x) is certainly not = 0 , therefore how can cot(x) be continious ?????????