Question

sin 2x + 2sin x = cos x + 1​

Answer 1

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

ОТВЕТ: п + 2пn ; (п/6) + 2пn ; (5п/6) + 2пn , n принадлежит Z.