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It is not defined as cosec 0 = 1/sin 0 = 1/0 which is undefined because this kind of division is just not defined in mathematics or if you see in books it will be given as infinity which is represented by sign "" .it is told as infinity as you see when you divide 1  by 0 you can never get a remainder as 0 so the quotient just goes on and on .
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Not defined as the reult would lead to infinity