Question

Упростите выражения:
a) (1/1+ctg^2a+cos^2a)*tg^2a
b)
(tg^2a/1+tg^a+cos^2a)*cos^a.

Answer 1

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)