2sinx-9cosx=7
4sin(x/2)cos(x/2)-9cos²(x/2)+9sin²(x/2)-7cos²(x/2)-7sin²(x/2)=0
2sin²(x/2)+4sin(x/2)cos(x/2)-16cos²(x/2)=0 /2ccos²(x/2)≠0
tg²(x/2)+2tg(x/2)-8=0
tg(x/2)=a
a²+2a-8=0
a1+a2=-2 U a1*a2=-8
a1=-4⇒tg(x/2)=-4⇒x/2=-arctg4+πn⇒x=-2arctg4+2πn
a2=2⇒tg(x/2)=2⇒x/2=arctg2+πn⇒x=2arctg2+2πn
x=2arctg2 -наим полож