Question

Prove csc^4x-2csc^2x+1=cot^4x

Answer 1

csc^4 x - 2 csc² x + 1 =
= 1 / sin^4 x - 2 / sin² x + 1 =
= ( 1 - 2 sin² x + sin^4 x ) / sin^4 x =
= ( sin² x - 1 )² / sin^4 x =
= ( cos² x )² / sin^4 x = cos^4 x / sin^ 4 x = cot ^4 x