Пошаговое объяснение:
1 + sin(x) - √3cos(x) = 0 ⇒ sin(x) - √3cos(x) = -1 ⇒ 2(1/2 sin(x) - √3/2 cos(x)) = -1 ⇒ 2sin(x-π/3) = -1 ⇒ sin(x - π/3) = -1/2 ⇒ x - π/3 = (-1)^(n+1) * π/6 + πn, n ⊂ Z ⇒ x = (-1)^(n+1) * π/6 + π/3 + πn, n ⊂ Z
При n = -1 x = π/6 + π/3 - π = -π/2 ⊄(0; π)
При n = 0 x = -π/6 + π/3 = π/6
При n = 1 x = π/6 + π/3 + π = 5π/2 ⊄ (0; π)
ответ: π/6
Пошаговое объяснение:
1 + sin(x) - √3cos(x) = 0 ⇒ sin(x) - √3cos(x) = -1 ⇒ 2(1/2 sin(x) - √3/2 cos(x)) = -1 ⇒ 2sin(x-π/3) = -1 ⇒ sin(x - π/3) = -1/2 ⇒ x - π/3 = (-1)^(n+1) * π/6 + πn, n ⊂ Z ⇒ x = (-1)^(n+1) * π/6 + π/3 + πn, n ⊂ Z
При n = -1 x = π/6 + π/3 - π = -π/2 ⊄(0; π)
При n = 0 x = -π/6 + π/3 = π/6
При n = 1 x = π/6 + π/3 + π = 5π/2 ⊄ (0; π)
ответ: π/6