2sin2x+cosx+4sinx+1=0
4sin(x)+cos(x)+4sin(x)*cos(x)+1=0
(4sin(x)+1)(cos(x)+1)=0
x=2πn-π, n∈Z
x=2πn+π, n∈Z
x=2πn-arcsin(1/4), n∈Z
x=2πn+π+arcsin(1/4), n∈Z
cos4x+4sin²x=1+2sin²2x
4sin²(x)+cos(4x)=2-cos(4x)
cos(2x)=cos(4x)
x=πn, n∈Z
x=-π/3+πn, n∈Z
x=π/3+πn, n∈Z
cos4x=1-2sin^2(2x) => 1-2sin^2(2x)+4sin^2(x)=1+2sin^2(2x) =>
4sin^2(x)=4sin^2(2x) => sin^2(2x)=4sin^2(x)*cos^2(x) =>
cos^2(x)=1/4 => cos(x)=1/2 =
x=arccos(1/2)+2πk k€Z
x= π /3+2 πk k€Z
2sin2x+cosx+4sinx+1=0
4sin(x)+cos(x)+4sin(x)*cos(x)+1=0
(4sin(x)+1)(cos(x)+1)=0
x=2πn-π, n∈Z
x=2πn+π, n∈Z
x=2πn-arcsin(1/4), n∈Z
x=2πn+π+arcsin(1/4), n∈Z
cos4x+4sin²x=1+2sin²2x
4sin²(x)+cos(4x)=2-cos(4x)
cos(2x)=cos(4x)
x=πn, n∈Z
x=-π/3+πn, n∈Z
x=π/3+πn, n∈Z
cos4x=1-2sin^2(2x) => 1-2sin^2(2x)+4sin^2(x)=1+2sin^2(2x) =>
4sin^2(x)=4sin^2(2x) => sin^2(2x)=4sin^2(x)*cos^2(x) =>
cos^2(x)=1/4 => cos(x)=1/2 =
x=arccos(1/2)+2πk k€Z
x= π /3+2 πk k€Z