Yes, a 4k TV can play 1080p video at 60fps. A 1080p video has 1920 horizontal pixels and 1080 vertical pixels, while a 4k TV has 3840 horizontal pixels and 2160 vertical pixels. When a 4k TV receives a 1080p signal, it downscales the image to fit its native resolution. This means that the 1080p video will be displayed on the 4k TV at its native resolution of 1920x1080, but the TV will use its own upscaling technology to fill in the extra pixels and make the image look as good as possible on the 4k screen. The 4k TV will be able to display the 1080p video at 60fps, which is the maximum frame rate for most Blu-ray discs and streaming services.