2cos²x+cos x-1=0, x принадлежит [-7 П/2; 2 П)

Cosx=a

2a²+a-1=0

D=1+8=9

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

-7π/2≤π+2πn≤2π

-7≤2+4n≤4

-9≤4n≤2

-9/4≤n≤1/2

n=-2⇒a=π-4π=-3π

n=-1⇒a=π-2π=-π

n=0⇒a=π

a2 = (-1+3) / 4=1/2⇒cosx=1/2⇒x=π/3+2πk U x=-π/3+2πm

-7π/2≤π/3+2πk≤2π

-21≤2+12k≤12

-23≤12k≤10

-23/12≤k≤5/6

k=-1⇒a=π/3-2π=-5π/3

k=0⇒a=π/3

-7π/2≤-π/3+2πm≤2π

-21≤-2+12m≤12

-19≤12m≤14

-19/12≤m≤7/6

m=-1⇒a=-π/3-2π=-7π/3

m=0⇒a=-π/3

m=1⇒a=-π/3+2π=5π/3