Question

Решить 1+sin2x=2sinx+cosx​

Answer 1

$1 + \sin(2x) = 2 \sin(x) + \cos(x) \\ 1 + 2\sin(x) \cos(x) - 2 \sin(x) - \cos(x) = 0 \\ \cos(x) (2 \sin(x) - 1) - (2 \sin(x) - 1) = 0 \\ (2 \sin(x) - 1)( \cos(x) - 1) = 0 \\ \\ \sin(x) = \frac{1}{2} \\ x1 = \frac{\pi}{6} + 2\pi \: n \\x 2 = \frac{5\pi}{6} + 2\pi \: n \\ \\ \cos(x) = 1 \\ x3 = 2\pi \: n$

n принадлежит Z.