2cos^2 5x - sin 5x cos 5x - sin^2 5x = 0 - вопрос №865761122555250 от Azdes 21.01.2020 15:42

Question

Алгебра: 2cos^2 5x - sin 5x cos 5x - sin^2 5x = 0

Azdes · Answer

2Cos^2 5x - Sin 5x Cos 5x - Sin^2 5x = 0 | : Сos² 5x≠ 0
2 - tg 5x - tg² 5x = 0
tg5x = t
t² + t - 2 = 0
по т. Виета корни -1 и 2
а) t = -1 б) t = -2
tg5x = -1 tg5x = -2
5x = -π/4 + πk , ∈Z 5x = arctg(-2) + πn , n ∈Z
x = -π/20 + πk/5 , k ∈Z x = -1/5*arctg2 + nπ/5 , n ∈Z