게 밝히다

state it openly, make it public

밝히다 is bringing something into the light — declaring a fact, revealing plans or feelings, clearing a matter up. -게 gives the manner, and these lines run from formal to shy: 확실하게 밝혀야 돼요 (this has to be stated definitively), 여러 차례 분명하게 밝혀봤습니다, 당당하게 밝혀요, alongside 수줍게 밝혀보는 감사의 마음 (shyly voicing his thanks). It keeps its literal sense too — 온 세상을 환하게 밝혀주니까요, lighting up the whole world.

Register: the 분명하게/확실하게 version is the language of public statements