let we consider,
sin^2 x + cos^2 x =1
(sin^2 x + cos^2 x)^2 =1^2
sin^4 x + cos^4x + 2 sin^2 x cos^2 x = 1
sin^4 x + cos^4x = 1 - 2 sin^2 x cos^2 x
since, sin^4 x + cos^4x = 1, then
1 = 1 - 2 sin^2 x cos^2 x
2 sin^2 x cos^2 x = 0
1/2(4 sin^2 x cos^2 x) = 0
1/2(2 sin x cos x) ^2= 0
->(2 sin x cos x) = sin 2 x, therefore
1/2 (sin 2 x)^2 = 0 ->sin^2 2x = 0
sin 2x = 0
2 x = 0, pi, 2 pi, 3pi, 4pi, ...
x = 0, pi/2, pi, (3pi)/2, 2pi. ...
x = (npi)/2, where n is an integer.