1)2sinx^2-6cosx+6=0
2) cos2x-2sinxcosx-3sin2x=0
3)sin4xcos3x+sin3xcos4x = -1
4) 7sin^2x-4sin2x+cos^2x=0
5) 4sinx-3=3cosx

12-2cos²x-6cosx+6=0cos²x+3cosx-4=0cosx=aa²+3a-4=0a1+a2=-3 U a1*a2=-4a1=-4⇒cosx=-4<-1 нет решенияa2=1⇒cosx=1⇒x=2πk,k∈z2Разделим на cos^2x1-2tgx-3tg²x=0tgx=a3a²+2a-1=0D=4+12=16a1=(-2-4)/6=-1⇒tgx=-1⇒x=-π/4+πk,k∈za2=(-2+4)/6=1/3⇒tgx=1/3⇒x=arctg1/3+πn,n∈z3sin(4x+3x)=-1sin7x=-17x=-π/2+2πk,k∈zx=-π/14+2πk/7,k∈z4Разделим на cos^2x7tg²x-8tgx+1=0tgx=a7a²-8a+1=0D=64-28=36a1=(8-6)/14=1/7⇒tgx=1/7⇒x=arctg1/7+πk,k∈za2=(8+6)/14=1⇒tgx=1⇒x=π/4+πn,n∈z58sin(x/2)cos(x/2)-3(1+cosx)=08sin(x/2)cos(x/2)-3*2cos²(x/2)=02cos(x/2)*(4sin(x/2)-3cos(x/2))=0cos(x/2)=0⇒x/2=π/2+πn,n∈z⇒x=π+2πn,n∈z4sin(x/2)-3cos(x/2)=0/cos(x/2)4tg(x/2)-3=0tg(x/2)=3/4x/2=arctg0,75+πk,k∈zx=2arctg0,75+2πk,k∈z