This is the 1290th most frequent Russian word.
пытаясь
"Trying" or "attempting."
The word 'пытаясь' is used as a present participle, describing the action of trying simultaneous to the action of falling.
Он падал, пытаясь удержать равновесие.
He was falling, trying to keep his balance.
Here, 'пытаясь' describes an effort made while performing another action, which is smiling.
Она улыбнулась, пытаясь скрыть свое волнение.
She smiled, trying to hide her nervousness.
In this example, 'пытаясь' is used to indicate the purpose of the action of writing a letter.