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

1

2-2cos²x-6cosx+6=0

cos²x+3cosx-4=0

cosx=a

a²+3a-4=0

a1+a2=-3 U a1*a2=-4

a1=-4⇒cosx=-4<-1 нет решения

a2=1⇒cosx=1⇒x=2πk, k∈z

2

Разделим на cos^2x

1-2tgx-3tg²x=0

tgx=a

3a²+2a-1=0

D=4+12=16

a1 = (-2-4) / 6=-1⇒tgx=-1⇒x=-π/4+πk, k∈z

a2 = (-2+4) / 6=1/3⇒tgx=1/3⇒x=arctg1/3+πn, n∈z

3

sin (4x+3x) = - 1

sin7x=-1

7x=-π/2+2πk, k∈z

x=-π/14+2πk/7, k∈z

4

Разделим на cos^2x

7tg²x-8tgx+1=0

tgx=a

7a²-8a+1=0

D=64-28=36

a1 = (8-6) / 14=1/7⇒tgx=1/7⇒x=arctg1/7+πk, k∈z

a2 = (8+6) / 14=1⇒tgx=1⇒x=π/4+πn, n∈z

5

8sin (x/2) cos (x/2) - 3 (1+cosx) = 0

8sin (x/2) cos (x/2) - 3*2cos² (x/2) = 0

2cos (x/2) * (4sin (x/2) - 3cos (x/2)) = 0

cos (x/2) = 0⇒x/2=π/2+πn, n∈z⇒x=π+2πn, n∈z

4sin (x/2) - 3cos (x/2) = 0/cos (x/2)

4tg (x/2) - 3=0

tg (x/2) = 3/4

x/2=arctg0,75+πk, k∈z

x=2arctg0,75+2πk, k∈z