Упростите sin^4 (x) - cos^4 (x) - sin^2 (x) + cos^2 (x)

sin^4x - cos^4x - sin^2x + cos^2x =

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

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

Вспомним, sin^2x + cos^2x = 1 = = >

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

= sin^2x - cos^2x - sin^2x + cos^2x =

= 0

Примечание

sin^2x и - sin^2x, а также cos^2x и - cos^2x взаимно уничтожились