2sin^2 * X-cosX-1=0 [3π; 4π]

2 (1-сos²x) - cosx-1=0

2-2cos²x-cosx-1=0

cosx=a

2a²+a-1=0

D=1+8=9

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

3π≤π+2πn≤4π

3≤1+2n≤4

2≤2n≤3

1≤n≤1,5

n=1⇒x=π+2π=3π

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

3π≤-π/3+2πn≤4π

9≤-1+6n≤12

10≤6n≤13

10/6≤n≤13/6

n=2⇒x=-π/3+4π=11π/3

3π≤π/3+2πn≤4π

9≤1+6n≤12

8≤6n≤11

8/6≤n≤11/6

нет решения