I have read that we use "have been" with the present perfect continuous as in the formula [has/have + been + present participle], e.g.,
You have been waiting here for two hours.
But sometimes I read sentences formed as [has/have + been + v3], e.g.,
the forest has been cleared .
I am confused about what the second formula is and in which cases we should use it.
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Are you asking for the difference between:
"They have been clearing the forest" and: "They have cleared the forest"?
If so, it's fairly simple: the continuous form ('-ing') implies 'continuation' i.e. the activity is still continuing or we simply don't know if the activity has finished yet. 'Have cleared' is clearly past tense. Therefore the activity ended.
Consider:
"They've been cleaning all day" (Have they finished? Don't know) "They cleaned all day" (Have they finished? Yes)
Present perfect simple or present perfect continuous? We use the present perfect simple, not continuous:
1 if the action is finished and complete. I've written a letter; I've learnt a new piece on the piano. I can play it now.
Present perfect continuous form
I've been learning Russian, but I can't speak it well.
2 if we want to say how often an action has happened. She's broken her leg three times.
3 with state verbs (like, love, know, etc). I've known Joe for years. (NOT I've been knowing Joe for years.)
