Question

2sin7x*cos2x+Sin4x=0 решите

Answer 1

2sin(7x)*cos(2x)+sin(4x)=0

2sin(7x)*cos(2x)+2sin(2x)*cos(2x)=0

2Cos(2x)*[sin(7x)+sin(2x)]=0

1.   cos(2x)=0

2x=pi/2+pi*n

x=pi/4+pi*n/2

 

2. sin(7x)+sin(2x)=0

2sin((7x+2x)/2)*cos((7x-2x)/2)=0

2sin(9x/2)*cos(5x/2)=0

sin(9x/2)*cos(5x/2)=0

a) sin(9x/2)=0

9x/2=pi*n

9x=2pi*n

x=2pi*n/9

б) cos(5x/2)=0

5x/2=pi/2+pi*n

5x=2pi/2+pi*n

x=2pi/10+pi*n/5