Решите уравнение sin x + cos x = 2sqrt(2)sin x cos x .
sin x + cos x = 2sqrt(2)sin x cos x sin(x + (pi)/(4)) = sin 2x [arrayl 2x = x + pi/4 + 2kpi 2x = pi - x - pi/4 + 2kpi array., k in Z [arrayl x = pi/4 + 2kpi x = pi/4 + 2kpi/3 array., k in Z x = pi/4 + 2kpi/3, k in Z.
\( x = \pi/4 + 2k\pi/3,\ k \in \mathbb{Z} \)