If someone coughs unintentionally the prayer becomes invalid; if the imam coughs i would'nt be certain if it was intentional but i have a strong feeling that the imam coughed intentionally, so i repeat the prayer to be on the safe side. Should i repeat the prayer if the imam coughs?

All perfect praise be to Allah, The Lord of the Worlds. I testify that there is none worthy of worship except Allah, and that Muhammad is His slave and Messenger.

Coughing during the prayer, whether by the Imam or someone else, does not invalidate the prayer. There is an authentic hadeeth on the authority of 'Abdullah ibn as-Saa'ib who said: 'I was with the Messenger of Allah on the day of the Conquest (of Makkah). He prayed in front of the Ka'bah. He took off his shoes and placed them to his left, and he started to recite Surat Al-Mu'minoon. When he reached the passage that mentions Moosa and 'Eisa he started coughing, then he bowed.'

Even if such an act is deliberate, it still does not invalidate the prayer as long as he does not articulate two letters in such a way that his action can be called speech. However, intentionally doing so is unlikely, especially for an Imam. Therefore, disregard any doubts and do not concern yourself with them, and do not repeat the prayer in such a situation.

Allah knows best.