Решите 6.sin2x/tgx=cosx 7.1-cosx+sinx/cosx=0 2sinx-√3/2cosx+1=0 п.с это числитель и знаменатель

6
2sinxcosx:sinx/cosx=cosx
2cos²x-cosx=0
cosx(2cosx-1)=0
cosx=0⇒x=π/2+πn,n∈z
cosx=1/2⇒x=+-π/3+2πk,k∈z
7
1-сosx+sinx=0
sin²x/2+cos²x/2-cos²x/2+sin²x/2+2sinx/2cosx/2=0
2sin²x/2+2sinx/2cosx/2=0
2sinx/2(sinx/2+cosx/2)=0
sinx/2=0⇒x/2=πn⇒x=2πn,n∈z
sinx/2+cosx/2=0/cosx/2
tgx/2+1=0
tgx/2=-1⇒x/2=-π/4+πk⇒x=-π/2+2πk.k∈z
cosx≠0⇒x≠π/2+πm,m∈z
x=2πn,n≠(1+2m)/4,n∈z U m∈z
x=-π/2+2πk.k≠(1+m)/2,k∈z U m∈z
8
(2sinx-√3)/(2cosx+1)=0
sinx=√3/2⇒x=π/3+2πn,n∈z U x=2π/3+2πk,k∈z
cosx≠-1/2⇒x≠+-2π/3+2πm,m∈z
x=π/3+2πn,n∈z