Question

Sin ( 5x - pi/3) = sin x помогите пожалуйста

Answer 1

Sin(5x-π/3)-sinx=0
$2sin \frac{5x-x- \pi /3}{2} *cos \frac{5x- \pi /3+x}{2} =0$$2sin \frac{4x- \pi /3}{2} *cos \frac{6x- \pi /3}{2} =0$
2sin(2x-π/6)*cos(3x-π/6)=0
sin(2x-π/6)=0
2x-π/6=πn
2x=πn+π/6
x=πn/2+π/12
cos(3x-π/6)=0
3x-π/6=πn/2
3x=πn/2+π/6
x=πn/6+π/18

Answer 2

Sin(5x-pi/3)-sinx=0 2sin(2x-pi/6)cos(3x-pi/6)=0 Sin(2x-pi/6)=0 2x-pi/6=pin , n e z 2x=pin+pi/6 , n e z x= pin/2+pi/12 , n e z Cos(3x-pi/6)=0 3x-pi/6=pi/2 +pin, n e z 3x=4pi/6+ pin , n e z x=4pi/18 + pin/3 , n e z