An NYPD detective allegedly showed up at the Ryder Cup golf tournament in full gear and claimed he was working security for President Trump — while out on sick leave, The Post has learned.

Det. Melvin Eng, who is now facing administrative charges for theft of services, may have even gotten away with the golf course ruse — had he not dropped his gun magazine in the grass in front of real security personnel, according to law enforcement sources and NYPD documents. 3

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“You’re out sick, what are you doing at the Ryder Cup?” one ticked off veteran cop said about Eng’s alleged stunt. “You can’t do that. And it’s theft of service because you went in for free and then you lied and said you worked for Donald Trump.”

Eng, 46, who is president of the NYPD Asian Jade Society, allegedly showe

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