Решить 2 уравнения

1) a) 1/tg²x+3/sinx+3=0 b) корни ур-я на [2p; 7p/2]

2) a) 1/sin²x-1/cos (3p/2-x) = 2 b) корни ур-я на [p; 5p/2]

1

сos²x/sin²x+3/sinx+3=0

sinx≠0

1-sin²x+3sinx+3sin²x=0

sinx=a

2a²+3a+1=0

D=9-8=1

a1 = (-3-1) / 4=-1⇒sinx=-1⇒x=-π/2+2πn, n∈z

2π≤-π/2+2πn≤7π/2

4≤-1+4n≤7

5≤4n≤8

5/4≤n≤2

n=2⇒x=-π/2+4π=7π/2

a2 = (-3+10/4=-1/2⇒sinx=-1/2

x=-π/6+2πk, k∈z U x=7π/6+2πm, m∈z

2π≤-π/6+2πk≤7π/2

12≤-1+12k≤21

13≤12k≤22

13/12≤k≤11/6

нет решения

2π≤7π/6+2πm≤7π/2

12≤7+12m≤21

5≤12m≤14

5/12≤m≤14/12

m=1⇒x=7π/6+2π=16π/6

2

sinx≠0

2sin²x-sinx-1=0

sinx=a

2a²-a-1=0

D=1+8=9

a1 = (1-3) / 4=-1/2⇒sinx=-1/2

x=-π/6+2πk, k∈z U x=7π/6+2πm, m∈z

π≤-π/6+2πk≤5π/2

6≤-1+12k≤15

7≤12k≤16

7/12≤k≤4/3

k=1⇒x=-π/6+2π=11π/6

π≤7π+2πm≤5π/2

6≤7+12m≤15

-1≤12m≤8

-1/12≤m≤2/3

m=0⇒x=7π/6

a2 = (1+3) / 4=1⇒sinx=1⇒x=π/2+2πn, n∈z

π≤π/2+2πn≤5π/2

2≤1+4n≤5

1≤4n≤4

1/4≤n≤1

n=1⇒x=π/2+2π=5π/2