ADJ

big, great
little
closely guarded, well-kept
a charming museum that is one of the city's best-kept secrets (= that not many people know about)
hidden, inner, innermost, intimate
That evening she had revealed many of her innermost secrets
open
Their affair is an open secret
dark, guilty, shameful, terrible
commercial, family, military, official, state, trade

VERB + SECRET

have
guard, keep
Can you keep a secret?
betray, divulge, let sb in on/into, reveal, tell sb
She let us into her secret?she'd got engaged
find out, uncover

SECRET + VERB

be/get out
How did the secret get out?

PREP

in ~
The film stars were married in secret to avoid publicity
~ about
There was some secret about the source of his wealth
~ from
I have no secrets from you

PHRASES

make no secret of the fact that … , make a secret of sth
He refuses to make any secret of his political allegiances

VERB + SECRET

reveal, tell sb

PREP

~ behind
She revealed the secret behind her extraordinary success
~ of
the secrets of staying healthy

PHRASES

the secret of (sb's) success