The first thing is to think about other ways of writing these functions. csc = 1/sin and cot = 1/tan
So: (1/sin) / (1/tan)
we also know tan is sin/cos, which will be better to work with because we can use the sine in the numerator.
(1/sin) / [1/(sin/cos)]
simplifying the right side, the division 1/(sin/cos) is the same as the multiplication in 1/1 * cos/sin = cos/sin
Now we have: (1/sin) / (cos/sin), which is the same as:
1/sin * sin/cos
crosscut the sins and we get: 1/cos
And, as we know, 1/cos is the same as secant, so our answer is sec(t).
Hope that helped and let me know if you have any questions!