Open iPhoto and have your iPhone connected. You'll have to 'Trust' your Mac computer on your iPhone before continuing.
Once connected you'll be able to see all your photos on your iOS device. At the top right-hand corner you'll see an Import button which you'll need to click in order to delete all the photos from your iPhone.
After hitting the import button and letting it complete (it might take some time if you've got a large collection of photos), you'll be prompted by iPhoto to Delete or Keep the photos on your iPhone. If you click on Delete X Items, the photos will be removed from your iPhone and won't even appear in your Recently Deleted album on your iOS device.
Once in iPhoto, you can view them, drag and drop them to another location on your Mac or delete them from iPhoto, by simply tapping Command + A to select all photos and then right clicking on any image to bring up a small dropdown menu which will have the option to send the photos to the Trash.
Once in Trash you can open the Trash on the left-hand column and view your binned photos. You can one-click Empty Trash and this will result in deleting all the photos from your Mac too.
Deleting from your Windows PC
If you're on a Windows PC, the process is very straight forward. Plug in your iPhone to your PC and ensure you Trust/Allow the PC to access your iPhone.
Once connected navigate to your iPhone's DCIM photo folder within Windows Explorer and simply select your photos you wish to delete or CTRL+A to select all and delete them through right clicking or SHIFT+DEL to permanently delete them off your iPhone.
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