Answer:
csc(theta)
Explanation:
we have
cot(theta)*sec(theta)
we know that
cot(theta)=cos(theta)/sin(theta)
sec(theta)=1/cos(theta)
csc(theta)=1/sin(theta)
so
substitute in the given expression
cot(theta)*sec(theta)=(cos(theta)/sin(theta))*(1/cos(theta))
Simplify
(cos(theta)/sin(theta))*(1/cos(theta))=1/sin(theta)
and
1/sin(theta)=csc(theta)
therefore
cot(theta)*sec(theta)=csc(theta)