Răspuns:
trigonometria era de faptmai mult...algebra::)))
2/3
74/81
nu garantez rezultatele, dar acesta poate fi mersul de calcul
am a[plicat a³+b³=(a+b)³-3ab(a+b)
si a²+b²=(a+b)²-2ab
Explicație pas cu pas:
(sin²X)³+ (cos²x)³= (sin²x+cos²x)³-3sin²xcos²x(sin²x+cos²x)=
1-3* (2sinxcox/2)²=1-3*sin²2x/4=1-(3/4) *(2/3)²=1-(3/4) *(4/9)=1-3/9=1-1/3=2/3
sin^8x+cos^8x=(sin^4x+cos^4x)² -2sin^4xcos^4x=
(sin^4x+cos^4x)²-2* (2sinxcosx/2) ^4=
(sin^4x+cos^4x)²-2* sin^4 (2x)/16=
(sin^4x+cos^4x)²-2*16/81*(1/16)=
(sin^4x+cos^4x)²-2/81=
((sin²x+cos²x)²-2sin²xcos²x)²-2/81
(1-2*(2/3)²*1/4)²-2/81=
(1-2/9)²-2/81=
1+4/81-1/9-2/81=
1+2/81-1/9=
1+2/81-9/81=
1-7/81=
74/81
