Verified answer

[csc²(x) - 1]/cot²(x)

[1/sin²(x) - 1]/[cos²(x)/sin²(x)]

[1/sin²(x) - sin²(x)/sin²(x)][sin²(x)/cos²(x)]

[1 - sin²(x)]/sin²(x)[sin²(x)/cos²(x)]

[1 - sin²(x)]/cos²(x)

Since sin²(x) + cos²(x) = 1, then 1 - sin²(x) = cos²(x):

cos²(x)/cos²(x) = 1

Recall that 1+cot²(x) = csc²(x).

From that, the expression you've given us comes out to be 1.