Y= (sin? x+cos？ x)？ -2 symptons? xcos？ x= 1-sin？ (2x)/2 = 1-( 1+cos4x)/4 = 3/4-(cos4x)/4

∴y'=sin4x,y''=4cos4x=4sin(4x+π/2),y'''=-4？ sin4x=4？ sin(4x+π)，

y ' ' ' =-4？ cos4x=4？ Sine (4x+3π/2) ......

Therefore, y (n) = 4 (n-1) sin (4x+(n-1) π/2) can be obtained.

=>y (n+1) = 4ncos (4x+(n-1) π/2) = 4sin (4x+nπ/2), ∴ The inductive hypothesis holds.

That is, y (n) = 4 (n-1) sin (4x+(n-1) π/2), (n≥ 1).