2(sin^4x + cos^4x ) = 1
2(( sin^2x)^2 + cos^2x ) = 1
2( ( 1 - cos^2x )^2 + cos^4x) = 1
2(( 1 -2cos^2x + cos^4x ) + cos^4x ) = 1
2( 1 - 2cos^2x + 2 cos^4x ) - 1 = 0
2 - 4cos^2x + 4cos^4x - 1 = 0
1-4cos^2x + 4cos^4x = 0
( cos^2x = t )
1 - 4t + 4t^2 = 0
( 1 - 2 t )^2 = 0
1 - 2t = 0
2t = 1
t = 1/2
cos^2x = 1/2
cosx = 1/sqrt2
cosx = sqrt2/2 ⇒
x = 45 degree, becouse cos45 = sqrt2/2