1) 12sin^2 x+4cosx-11=0 на промежутке [3 п: 4 п]

2) cos2x-sin^2 x=0,25 на промежутке [п/2; 3 п]

3) (8sin^2 x=14sinx+5) * log (по основанию 3) (cosx) = 0

1) 12-12cos²x+4cosx-11=0

12cos²x-4cosx-1=0

cosx=a

12a²-4a-1=0

D=16+48=64

a1 = (4-8) / 24=-1/6⇒cosx=-1/6⇒x = + - (π-arccos1/6) + 2πn

a2 = (4+8) / 24=1/2⇒cosx=1/2⇒x=+-π/3+2πn

x=7π/2-arccos1/6; 23π/6

2) 1-2sin²x-sin²x=1/4

3sin²x=3/4

sin²x=1/4

(1-cos2x) / 2=1/4

1-cos2x=1/2

cos2x=1/2

2x=+-π/3+2πn

x=+-π/6+πn

3) cosx>0⇒x∈ (-π/2+2πn; π/2+2πn)

8sin²x+14sinx+5=0

sinx=a

8a²+14a+5=0

D=196-160=36

a1 = (-14-6) / 16=-15/8⇒sinx=-15/8∉[-1; 1]

a2 = (-14+6) / 16=-1/2⇒sinx=-1/2⇒x=-π/6+2πn

log (3) cosx=0

cosx=1⇒x=2πn