Задача 67495 ...

639426c48ea9585e4d6e9910

10.12.2022 09:32:29

????????????2???? + 2???????????????? − √3???????????????? = √3

626fab9a354ab65fb2f43abb

10.12.2022 10:08:25

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sin 2x + 2sin x - sqrt(3)cos x - sqrt(3) = 0
Раскладываем на множители:
2sin x*cos x + 2sin x - sqrt(3)*(cos x + 1) = 0
2sin x*(cos x + 1) - sqrt(3)*(cos x + 1) = 0
(2sin x - sqrt(3))(cos x + 1) = 0
1) 2sin x - sqrt(3) = 0
sin x = sqrt(3)/2
x1 = π/3 + 2πn, n ∈ Z
x2 = 2π/3 + 2πn, n ∈ Z
2) cos x + 1 = 0
cos x = - 1
x3 = π + 2πk, k ∈ Z