Question

csc^4x-cot^4x=csc^2x+cot^2x

Answer 1

\[(csc^2x)^2 - (cot^2x)^2\]= \[(csc^2x+cot^2x)(csc^2x-cot^2x)\]

Answer 2

let the first tem aside, I just manipulate the second term and make it =1 so you get the answer, right?

Answer 3

\[= \frac{ 1 }{ \sin^2x }-\frac{ \cos^2x }{ \sin^2x }=\frac{ 1-\cos^2x }{ \sin^2x}= \frac{ \sin^2x }{ \sin^2x }=1\]
so your stuff is proved