Do you trust in cheap handheld oscilloscope

Trust seems like the wrong word for a scope, while in its oldest form its a very raw simple instrument, but in practice its easy to use it incorrectly and/or make bad assumptions about what you see. In the modern form, a digital scope, its fly by software regardless of how simple the circuits might be, so there is no way of knowing if some “feature” is showing something or hiding something of value.

My experience is that the chance of problems being user error vs issues with the scope are about 10 to 1, and not enhanced much by the quality of the scope.

Know how the scope works, what its limits are, how to use it, and what to look for in the signal and just about anything should be ok. Some like Fluke put a lot of smarts in the tool so they are simple to use, but that nice Fluke is like a grand or more, and very popular among those that use them in their work.