04.02.2021 15:34:02
Алгебра 10-11 класс
10 баллов
Найти значение выражения
sin(α+β)×sin(α -β) если α=45°, β=15°
(sin α+sin β)^2-(sin α-sin β)^2при α=30°, β =45°
sin(α+β)×sin(α -β) если α=45°, β=15°
(sin α+sin β)^2-(sin α-sin β)^2при α=30°, β =45°
Ирина Каминкова
0
04.02.2021 16:14:34
sin(α+β)×sin(α -β) = sin(45°+15°)×sin(45° -15°) = sin 60° × sin 30° = (√3/2) * (1/2) = √3/4
(sin α+sin β)^2-(sin α-sin β)^2 =
=(sin ^2 α+sin^2 β + 2*sin α×sin β) - (sin ^2 α+sin^2 β - 2*sin α×sin β)=
= 4*sin α×sin β = 4*sin 30° sin 45° = 4*(1/2)*(√2/2) = √2
(sin α+sin β)^2-(sin α-sin β)^2 =
=(sin ^2 α+sin^2 β + 2*sin α×sin β) - (sin ^2 α+sin^2 β - 2*sin α×sin β)=
= 4*sin α×sin β = 4*sin 30° sin 45° = 4*(1/2)*(√2/2) = √2
Ответ эксперта
