Use difference of squares. (I'm leaving out the "x" part)
csc^4 - cot^4 = (csc^2 + cot^2)(csc^2 - cot^2)
From here, we should recognize one of the trig identities:
1 + cot^2 = csc^2
or rewritten as:
1 = csc^2-cot^2
So we can substitute the above into our previous equation:
(csc^2 + cot^2)(csc^2 - cot^2)
= (csc^2 + cot^2)(1)
= csc^2 + cot^2
And we have proven it. :)
