prove: sin^4@-cos^4@ = sin^2@-cos^2@

sin(A)^4 - cos(A)^4

=   ( sin²(A) - cos²(A) )( sin²(A) + cos²(A) )            Since  sin²(A) - cos²(A) = 1:

=   ( sin²(A) - cos²(A) )(1)

=   sin²(A) - cos²(A) 

sin^4@-cos^4@ = sin^2@-cos^2@    ....I'll use "x" instead of "@"......so we have

sin^4x - cos^4x       factor  this

(sin^2x - cos^2x) (sin^2x + cos^2x)       

But note.....  (sin^2x + cos^2x) = 1

So

(sin^2x - cos^2x) (1) =

(sin^2x - cos^2x)    and this equals the right hand side