2sin2x+cosx+4sinx+1=0 4sinxcosx+cosx+4sinx+1=0 4sinx(cosx+1)+(cosx+1)=0 (cosx+1)(4sinx+1)=0 1) cosx+1=0 cosx=-1 x=π+2πn,n∈Z 2) 4sinx+1=0 sinx=-1/4 x=(-1)^k•arcsin(-1/4)+πk x=(-1)^(k+1)•arcsin(1/4)+πk,k∈Z
вроде так
2sin2x+cosx+4sinx+1=0
4sinxcosx+cosx+4sinx+1=0
4sinx(cosx+1)+(cosx+1)=0
(cosx+1)(4sinx+1)=0
1) cosx+1=0
cosx=-1
x=π+2πn,n∈Z
2) 4sinx+1=0
sinx=-1/4
x=(-1)^k•arcsin(-1/4)+πk
x=(-1)^(k+1)•arcsin(1/4)+πk,k∈Z
вроде так