It is possible, but I suggest you check each posting. If you sold an option short, and it expired, the zero cost basis would be correct.
However, from time to time the broker does not know what the cost basis actually was. In that case you would be incorrectly taxed on the full amount of the proceeds.
If you do have transactions that do require a cost basis, this tool may help.
You may be able to use Historical Stock Quote Prices - MarketWatch to determine the original value.
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