Verify the identity: cot^3t/csct = cost(csc^2t-1)

We know that cot = cos/sin
then cot^3 = cos^3 / sin ^3
we also know that csc = 1/sin
then 1/csc = sin
cot^3t/csct =(cos^3t / sin^3t) * sint =cos^3t / sin^2t
1+cot^2 = csc^2
csc^2 -1 = cot^2
cost(csc^2t-1) =cost(cot^2t)
cost( cos^2t/sin^2t) =cos^3t/sin^2t
It implies that both sides are equal

hope it helps