x=2kπ/3, k∈Z,
x=kπ, k∈Z.
Объяснение:
2*sin(2x)/cos(3x)=tan(x), x не равно π/6 + kπ/3, k∈Z
2* 2sin(x)cos(x)/4cos(x)³-3cos(x)=sin(x)/cos(x)
2*2sin(x)cos(x)/cos(x)*(4cos(x)²-3=sin(x)/cos(x)
2*2sin(x)/4cos(x)²-3=sin(x)/cos(x)
4sin(x)cos(x)=sin(x)*(4cos(x)²-3)
4sin(x)cos(x)=4sin(x)=4sin(x)cos(x)²-3sin(x)
4sin(x)cos(x)-4sin(x)cos(x)²+3sin(x)=0
sin(x)*(4cos(x)-4cos(x)²+3)=0
sin(x)*(-4cos(x)²+4cos(x)+3=0
sin(x)*(-4cos(x)²+6cos(x)-2cos(x)+3)=0
sin(x)*(-2cos(x)*(2cos(x)-3)-(2cos(x)-3))=0
sin(x)(-(2cos(x)-3)*(2cos(x)+1))=0
-sin(x)*(2cos(x)-3)*(2cos(x)+1=0
sin(x)*(2cos(x)-3)*(2cos(x)+1=0
sin(x)=0
2cos(x)-3=0
2cos(x)+1=0
x=kπ, k∈Z
x не принадлежит R
x=2π/3+2kπ, k∈Z
x=4π/3+2kπ, k∈Z
x=kπ, k∈Z,
x не равен π/6+kπ/3, k∈Z
x=2kπ/3, k∈Z,
x=kπ, k∈Z.
Объяснение:
2*sin(2x)/cos(3x)=tan(x), x не равно π/6 + kπ/3, k∈Z
2* 2sin(x)cos(x)/4cos(x)³-3cos(x)=sin(x)/cos(x)
2*2sin(x)cos(x)/cos(x)*(4cos(x)²-3=sin(x)/cos(x)
2*2sin(x)/4cos(x)²-3=sin(x)/cos(x)
4sin(x)cos(x)=sin(x)*(4cos(x)²-3)
4sin(x)cos(x)=4sin(x)=4sin(x)cos(x)²-3sin(x)
4sin(x)cos(x)-4sin(x)cos(x)²+3sin(x)=0
sin(x)*(4cos(x)-4cos(x)²+3)=0
sin(x)*(-4cos(x)²+4cos(x)+3=0
sin(x)*(-4cos(x)²+6cos(x)-2cos(x)+3)=0
sin(x)*(-2cos(x)*(2cos(x)-3)-(2cos(x)-3))=0
sin(x)(-(2cos(x)-3)*(2cos(x)+1))=0
-sin(x)*(2cos(x)-3)*(2cos(x)+1=0
sin(x)*(2cos(x)-3)*(2cos(x)+1=0
sin(x)=0
2cos(x)-3=0
2cos(x)+1=0
x=kπ, k∈Z
x не принадлежит R
x=2π/3+2kπ, k∈Z
x=4π/3+2kπ, k∈Z
x=2kπ/3, k∈Z,
x=kπ, k∈Z,
x не равен π/6+kπ/3, k∈Z
x=2kπ/3, k∈Z,
x=kπ, k∈Z.