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

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.