As far as I'm aware you can't install LaTeX on the iPad because of the restrictions that Apple put on it. However, tex documents can be edited and compiled using Tex Touch . The editor is installed on the iPad and the tex document is then compiled online at TeX Cloud. I haven't used Tex Touch myself so I can't comment on how well it works.
That being said, however, it seems that many apps do support screen mirroring. The following list seems to be quite extensive and includes a few apps that can display PDF, which is what you would need to display TeX output. Pipiro notes in the comments that Goodnotes can also mirror on the iPad 1.
Subsequent iPad models support mirroring for all apps, so you should be able to use your favourite PDF viewer to display PDFs on current versions of the iPad.
Best Answer
As far as I'm aware you can't install LaTeX on the iPad because of the restrictions that Apple put on it. However, tex documents can be edited and compiled using Tex Touch . The editor is installed on the iPad and the tex document is then compiled online at TeX Cloud. I haven't used Tex Touch myself so I can't comment on how well it works.