ПОМОГИТЕЕЕ 1. (tg a + ctg a) * sin a * cos a 2. sin^2 a * cos^2 a (tg^2 a + ctg^2 a + 2)

Question

ПОМОГИТЕЕЕ

1. (tg a + ctg a) * sin a * cos a
2. sin^2 a * cos^2 a (tg^2 a + ctg^2 a + 2)

Answer 1

1)=( sin a / cos a + cos a/ sina) * sina *cosa= sin^2a + cos^2 a = 1
тут раскрыли скобки
2) = sin^4 a + cos^4 a + 2sin^2acos ^2a=
= (1-cos^2 a)^2 + cos^4 a + 2 (1-cos^2)cos^2=
=1 - 2 cos^2 a + 2cos^4 + 2 (cos^2-cos^4)=
= 1 - 2 cos^2 a + 2cos^4 + 2 cos^2 a - 2cos^4 =
= 1