csc is a trigonometry function cosec, which is  1/sin.


You are given that   csc(t) = ,   where "t"  is some angle  and  "a"  and  "b" are some real numbers.

and "they" want you find  cot(t). 


In other words, you are given that  sin(t) =   (inverted ratio),

and "they" want you find  cot(t). 


As you know  (or must know)  cot(t) = .


You just know the denominator  sin(t):  it is just given and is equal to  .


Next step you need to do is to compute  cos(t).


It is easy:  cos(t) =  = .


Therefore, you answer is:  cot(t) = .


Answer.   cot(csc^-1(a/b)) = cot(t) = cot(arccsc(a/b) = .