Найти: cos(α/2+π)cos(π/2+α/2), если cosα=−3/5, α∈[−3π/2;−π]

Question

Найти: cos(α/2+π)cos(π/2+α/2), если cosα=−3/5, α∈[−3π/2;−π]

Answer 1

Упрощаем:
cos ( a/2 +П) cos(П/2 + а/2) = -cosa/2 × (-sin a/2) = 1/2×Sina
sin^2a = 1 - 9/25 = 16/25
Sina = 4/5
1/2× 4/5 =2/5 = 0,4
Ответ: 0,4.