Question 1031795
let a = opposite side of angle x.
let b = adjacent side of angle x.


tanx = opposite side / adjacent side = a/b


cotx = adjacent side / opposite side = b/a


if you take 1 and divide it by tanx, you get 1 / tanx = 1 / (a/b)


since 1 / (a/b) is equal to 1 * (b/a), you get 1 / tanx = b/a


since b/a is equal to cotx, you get 1/tanx = cotx.


that's your proof.