Question

Sinx-sin2x+sin5x+sin8x=0 Решите уравнение.

Answer 1

Sin5x+sinx+sin8x -sin2x =0;
2sin3xcos2x +2sin3xcos5x=0 ;
2sin3x(cos5x +cos2x) =0;
sin3xcos7x/2*cos3x/2 =0 ;
sin3x=0 ⇒3x =π*k ⇔x =π/3*k ,k∈Z.
cos7x/2=0⇒7x/2 =π/2+π*k ⇔x =π/7+2π/7*k ,k∈Z.
cos3x/2 =0 ⇒3x/2  =π/2+π*k ⇔x =π/3+2π/3*k ,k∈Z.