In Salesforce Production Environment The DEL option is not displayed for classes.
Follow the below steps:
Go To Sandbox and delete triggers form there and Also delete the Test Methods that test the Class/Trigger.
Go to Eclipse and do a Refresh from Server. This will make the files disappear within Eclipse.
Then deploy to Production, ticking Delete next to the files in your Deployment Plan. (For safety, always Deselect All when deploying, then sort by Type. Only then tick which files to deploy, since choosing the wrong ones could cripple Production.