Verb + infinitive, no preposition
avoir beau
no preposition
The constructions
no prepositionavoir beau + infinitif
J'ai beau chercher, je ne trouve rien.
Why
Avoir beau followed directly by an infinitive expresses concession: j'ai beau essayer means however much I try, in vain. Always at the start of the sentence, always without a preposition.
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