Question

Способом разложения на множители sin2x+√3×cosx=2sinx+√3

Answer 1

Sin2x + √3cosx = 2sinx + √3
2sinxcosx - 2sinx + √3cosx - √3 = 0
2sinx(cosx - 1) + √3(cosx - 1) = 0
(2sinx + √3)(cosx - 1) = 0
1) 2sinx + √3 = 0
2sinx = -√3
sinx = -√3/2
x = -π/3 + 2πk, k ∈ Z U x = 4π/3 + 2πk, k ∈ Z
2) cosx - 1 = 0
cosx = 1
x = 2πn, n ∈ Z
Ответ: x =-π/3 + 2πk, k ∈ Z; 4π/3 + 2πk, k ∈ Z; 2πn, n ∈ Z.