Question

тригонометрические уравнения,срочно!

Answer 1

1
sinx=a
2a²-a-1=0
D=1+8=9
a1=(1-3)/4=-1/2⇒sinx=-1/2⇒x=(-1)^(n+1)*π/6+πn,n∈z
a2=(1+3)/4=1⇒sinx=1⇒x=π/2+2πn,n∈z
2
4sinxcosx-3sin²x-sin²x-cos²x=0
4sin²x-4sinxcosx+cos²x=0/cos²x
4tg²x-4tgx+1=0
(2tgx-1)²=0
2tgx=1
tgx=1/2
x=arctg1/2+πn,n∈z
3
sin(5π/6+x/2)=-√3/2
5π/6+x/2=-π/3+2πn U 5π/6+x/2=4π/3+2πn
x/2=-7π/6+2πn U x/2=π/2+2πn
x=-7π/3+4πn U x=π+4πn,n∈z