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