You can install a keylogger, then you can watch not only the history of visits, but also read messages, track movements and listen to the sound around the phone
Look for his photo on Yandex. Select pictures. Tap on the camera. Next, select a photo of your person. If he is somewhere, then all links with site addresses are displayed. Follow the link and look. Works even on body parts, not only by the photo of the face. True, it will be unpleasant for you to find him where you did not expect.
Ask. The most correct and honest option.
Hypothetically, there is such a thing as browser history, but climbing on it in a guy's computer is a rather sneaky act towards him.
If he catches you for this will give you a header and will be right
You can view the history of site visits from your computer. Go to the browser and in the upper right corner, click on three dots, a sign will pop up in which you need to select the "history" item, these will be the sites that the person visited, you just need to take into account that this history of visits can be cleared and then you will not look at anything.