trig 數學問題

　sin^4 x - cos^4 x
= (sin² x)² - (cos² x)²
= (sin² x + cos² x)(sin² x - cos² x)　　　[ ∵ a² - b² = (a + b)(a - b) ]
= sin² x - cos² x 　　　　　　　　　　 [ ∵ sin² x + cos² x = 1 ]

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

By law,
sin^2 x + cos^2 = 1
a^2 - b^2 =(a+b)(a-b)