Упростите выражения:

a) (1/1+ctg^2a+cos^2a) * tg^2a

b)

(tg^2a/1+tg^a+cos^2a) * cos^a.

1)

1/cos^2 (a) - tg^2 (a) - sin^2 (a) =

=1/cos^2 (a) - sin^2 (a) / cos^2 (a)) - sin^2 (a) =

=[1 - sin^2 (a) ]/cos^2 (a)) - sin^2 (a) =

=cos^2 (a) / cos^2 (a)) - sin^2 (a) =

=1--sin^2 (a) = cos^2 (a)

2)

cos^2 (a) + ctg^2 (a) - 1/sin^2 (a) =

=cos^2 (a) + [cos^2 (a) - 1]/sin^2 (a) =

=cos^2 (a) - sin^2 (a) ]/sin^2 (a) =

=cos^2 (a) - 1 = - sin^2 (a)

3)

1/cos^2 (a) - tg^2 (a) (cos^2 (a) + 1) =

=1/cos^2 (a) - sin^2 (a) - sin^2 (a) / (cos^2 (a) =

= (1 - sin^2 (a)) / cos^2 (a) - sin^2 (a) =

=1-sin^2 (a) = cos^2 (a)