verb
1
BAD : You should not believe in everything you hear.
GOOD : You should not believe everything you hear.
BAD : She couldn't believe in what was happening to her.
GOOD : She couldn't believe what was happening to her.
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believe in sth = (1) accept that something exists: 'Do you believe in ghosts?' 'James still believes in Father Christmas.'
(2) think that something is good: 'I don't believe in capital punishment.' 'I believe in getting a good night's sleep before an examination.'
believe sth = accept that something is true or real: 'I believe every word she said.' 'I couldn't believe what I was seeing.'
2
BAD : I could hardly believe in my eyes.
GOOD : I could hardly believe my eyes.
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could not/hardly believe your ears/eyes (WITHOUT in )
3
BAD : I deeply believe that tourists will stop coming here.
GOOD : I firmly believe that tourists will stop coming here.
BAD : My brother deeply believes in freedom of speech.
GOOD : My brother strongly believes in freedom of speech.
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firmly/strongly/fervently/sincerely/truly believe (NOT deeply ): 'I sincerely believe that he had no connection with the crime.'