Question

Помогите решить пример:

$sin(2x)*cos(x)+cos(2x)*sin(x)=0$

Answer 1

Sin2xCosx + Cos2xSinx = 0
2SinxCosxCosx + Cos2xSinx = 0
Sinx(2Cos²x + Cos2x) = 0
Sinx(2Cos²x + 2Cos²x - 1) = 0
Sinx(4Cos²x - 1) = 0
Sinx = 0                                          4Cos²x -1= 0
x = πn , n ∈ z                                  4Cos²x = 1
                                                        Cos²x = 1/4
$Cosx = frac{1}{2}$                              $Cosx = - frac{1}{2}$
$x = + - frac{ pi }{3} +2 pi n$,n∈z       $x = + - frac{2 pi }{3} +2 pi n,$n∈z