sin^4 x+ cos^4 x=sin x * cos x
sin^4 x + 2sin^2 x * cos^2 x + cos^4 x = 2 sin^2 x cos^2 x + sinx*cos x
(sin^2 x + cos^2 x)^2=2sinxcosx(2sinxcosx + 1)/2
2 = sin 2x * (sin 2x + 1)
sin 2x = t, t in [-1,1]
t^2+t-2=0
t=1
sin 2x = 1
2x = pi/2 + 2*pi*k, k in Integers
x = pi/4 + pi*k, k in Integers
sin^4 x+ cos^4 x=sin x * cos x
sin^4 x + 2sin^2 x * cos^2 x + cos^4 x = 2 sin^2 x cos^2 x + sinx*cos x
(sin^2 x + cos^2 x)^2=2sinxcosx(2sinxcosx + 1)/2
2 = sin 2x * (sin 2x + 1)
sin 2x = t, t in [-1,1]
t^2+t-2=0
t=1
sin 2x = 1
2x = pi/2 + 2*pi*k, k in Integers
x = pi/4 + pi*k, k in Integers