Sin ^4 X+cos ^4 X+sin 2x=7\5sin⁴x+2sin²xcos²x+cos⁴x-2sin²xcos²x+sin2x=7/5
(sin²x+cos²x)²-(sin²2x)/2+sin2x-7/5=0
10-5sin²2x+10sin2x-14=0
5sin²2x-10sin2x+4=0
sin2x₁=(10+√(100-80))/10=1+√5/5 >1 не подходит
sin2x=1-√5/5 2x=(-1)^k×arcsin(1-√5/5)+πk x=(-1)^k×(arcsin(1-√5/5))/2+πk/2 k∈Z