Решите уравнение sin4 x=cos^4 x-sin^4 x

sin4 x=cosx^{4}-sinx^{4}

sin4x=(cosx^{2}-sinx^{2})(cosx^{2}+sinx^{2})

sin4x=(cosx^{2}-sinx^{2})*1

sin4x=cos2x

sin(2*2x)-cos2x=0

2sin2x*cos2x-cos2x=0

cos2x(2sin2x-1)=0

cos2x=0                                           2sin2x-1=0

2x=+-pi/2 +2pi*n                              2sin2x=1

x=+-pi/4 +pi*n, n принадл.Z             sin2x=1/2

                                                      2x=(-1)^{n}pi/6+pi*n

                                                      x=(-1)^{n}*pi/12+pi*n/2, n принадл.Z