verify (csc^4-1)/cot^2x=2+cot^2x

Question

So this is what I have so far on the left side

(csc^2x+1)(cscx+1)(cscx-1)/cot^2x
=(csc^2x+1)(cot^2x)/cot^2x

i think I'm doing something wrong. Please help!

Answer 1

recall that 1 + cot^2 x = csc^2 x
as a variation of the Pythagorean identity

so
LS = (csc^2x+1)(csc^2 x-1)/cot^2x
= (1 + cot^2 x + 1)(1 + cot^2 x -1)/cot^2 x)
= 2 + cot^2 x
= RS