Question

Sin^6a+cos^6a-3sin^2a-3/1+ctg^2a

Answer 1

Сначала числитель:
(Sin^6 a +cos^6 a) + (-3Sin^2 a -3) =
 =(Sin^2 a + Cos^2 a)( Sin^4 a -Sin^2 aCos^2 a + Cos^4 a)  -3 ( Sin^2 a +1)=
= Sin^4 a - Sin^2 aCos^2 a + Cos^4 a  + 3Sin^2 aCos^2 a - 3Sin^2 aCos^2 a -
-3(Sin^2 a +1)= (Sin^4 a + 2Sin^2 aCos^2 a + Cos^4 a) -3Sin^2 aCos^2 a -
-3(Sin^2 a +1)=
=(Sin^2 a  + Cos^2 a)² - 3Sin^2 aCos^2 a -3(Sin^2 a + 1)=
=1 -3(Sin^2 aCos^2 a + Sin^2 a +1)=
=1 -3Sin^2 aCos^2 a -3Sin^2 a -3=-3Sin^2 aCos^2 a -3Sin^2 a -2=
= -3Sin^2 a(Cos^2 a +1) - 2
Знаменатель:
1 + Ctg^2 a = 1/Sin^2 a
Делим числитель на знаменатель.