Question

Корень из 3 •sin3x=cos3x+1

Answer 1

√3 *sin 3x = cos 3x + 1
√3 *sin 3x - cos 3x = 1      Делить на 2
$\frac{ \sqrt{3}}{2}sin(3x) - \frac{1}{2} cos(3x)= \frac{1}{2}$
cos π/6 * sin 3x - sin π/6 * cos 3x = 1/2
sin (3x - π/6) = 1/2

1) 3x - π/6 = π/6 + 2πn
    3x = π/3 + 2πn
    $x_1 = \frac{ \pi }{9} + \frac{2 \pi n}{3}$

2) 3x - π/6 = 5π/6 + 2πk
    3x = 5π/6 + π/6 + 2πk
    3x = π + 2πk
    $x_2 = \frac{ \pi }{3} + \frac{2 \pi k}{3}$

Ответ: $x_1 = \frac{ \pi }{9} + \frac{2 \pi n}{3}$; $x_2 = \frac{ \pi }{3} + \frac{2 \pi k}{3}$; n,k∈Z