we have that
case A) tan x = cos x/ sin x--------> is not a identity
the correct identity is
tan x=sin x/cos x------> is a ratio identity
case B) csc x = 1/ sin x-------> is a identity (Reciprocal identity)
case C) cot x = 1/ tan x ------> is a identity (Reciprocal identity)
case D) sec x = 1/ csc x-------> is not a identity
the correct identity is
sec x=1/cos x-------> is a Reciprocal identity
therefore
the answer is
B) csc x = 1/ sin x
C) cot x = 1/ tan x