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.