Question

Дано sina=3/5, ae(п/2:п) найти cos2a

Answer 1

Вторая четверть $alpha in [ pi /2; pi ]$
$cos2 alpha =cos^2 alpha -sin^2 alpha \ sin alpha =3/5 \ sin^2 alpha +cos^2 alpha =1=>cos^2 alpha = \ =1-sin^2 alpha=1-(3/5)^2=1-9/25=16/25 \ cos2 alpha =cos^2 alpha -sin^2 alpha=16/25-9/25=7/25 \ cos2 alpha =7/25$