Question

Доказать тождество. Даю 100 баллов. с решением

Answer 1

$sin^4(a)+cos^4(a)-sin^6(a)-cos^6(a)=sin^2(a)cos^2(a)\\(1-sin^2(a))*sin^4(a)+cos^4(a)-cos^6(a)=sin^2(a)cos^2(a)\\cos^2(x)sin^4(a)+cos^4(a)-cos^6(a)=sin^2(a)cos^2(a)\\((sin^2(a)-cos^2(a))(sin^2(a)+cos^2(a))+cos^2(a))*cos^2(a)=\\=sin^2(a)cos^2(a)\\(-(cos^2(a)-sin^2(a)+cos^2(a))cos^2(a)=sin^2(a)cos^2(a)\\(-(cos^2(a)-sin^2(a))+cos^2(a))cos^2(a)=sin^2(a)cos^2(a)\\(-cos^2(a)+sin^2(a)+cos^2(a))cos^2(a)=sin^2(a)cos^2(a)\\sin^2(a)cos^2(a)=sin^2(a)cos^2(a)$

Answer 2

Преобразуем левую часть
(sin^4a-sin^6a)+(cos^4a-cos^6a)=sin^4a(1-sin^2a)+cos^4a(1-cos^2a=
=sin^4a*cos^2a+cos^4a*sin^2a=sin^2a*cos^2a*(sin^2a+cos^2a)=
=sin^2a*cos^2a *1=sin^2a*cos^2a
sin^2a*cos^2a=sin^2a*cos^2a