<span>Cos^6x+Sin^6x-Сos^2 2x=1/16
сумма кубов
(Cos</span>²x + Sin²x)( Cos⁴x - Sin²xCos²x + Sin⁴x) - Cos² 2x=
= Cos⁴x - Sin²xCos²x + Sin⁴x - Cos²2x=
= Cos⁴x - Sin²xCos²x + Sin⁴x - ( Cos²x - Sin²x)²=
=Cos⁴x - Sin²xCos²x + Sin⁴x - Cos⁴x +2Sin²xCos²x - Sin⁴x =
=Sin²xCos²x= 4/4 Sin²xCos²x = 1/4 Sin²2x
1/4 Sin²x = 1/16
Sin²x = 1/4
Sinx = +-1/2
x = (-1)ⁿ arcSin(+-1/2) + nπ, n ∈ Z
Можно 2/8 = 2/4 , 5/10 = 1/2 , 3/4 - , 7/21 = 1/3, 6/9 = 2/3 , 1/5 - , 8/9 - , 16/20 4/5 , 4/5 - , 12/16 = 3/4 , 5/75 1/15