6)2-2cos²x+5cosx+1=0
2cos²x-5cosx-3=0
cosx=a
2a²-5a-3=0
D=25+24=49
a1=(5-7)/4=-1/2⇒cosx=-1/2⇒x=+-2π/3+2πn
a2=(5+7)/4=3⇒cosx=3∉[-1;1]
7)sin²x+cos²x-4sinxcosx-6cos²x=0 /cos²x≠0
tg²x-4tgx-5=0
tgx=a
a²-4a-5=0
a1+a2=4 U a1*a2=-5
a1=-1⇒tgx=-1⇒x=-π/4+πn
a2=5⇒tgx=5⇒x=arctg5+πn
8)1+sin2x=cos2x
sin²x+cos²x+2sinxcosx-cos²x+sin²x=0 /cos²x≠0
2tg²x+2tgx=0
2tgx(tgx+1)=0
tgx=0⇒x=πn
tgx=-1⇒x=-π/4+πn
9)-2sinx/2cos5x/2=0
sinx/2=0⇒x/2=πn⇒x=2πn
cos5x/2=0⇒5x/2=π/2+πn/2⇒x=π/5+2πn/5