log8( 2 sin²х - 9 sin( (3π)/2-х )+5 )=1/3
(log(5+9cosx+2sin²x)/log8 =1/3
log(5+9cosx+2sin²x=log8/3
log(5+9cosx+2sin²x=log2
5+9cosx+2sin²x=2
-(cosx-5)(2cosx+1)=0
(cosx-5)(2cosx+1)=0
cosx-5=0; 2cosx+1=0
cosx=5; 2cosx+1=0
2cosx+1=0
2cosx= -1
cosx= -1/2
x= 2πn₁+2π/3, n₁ ∈ Z
Для корня π/2 + πn, n ∈ Z
-4π ≤ π/2 + πn ≤ -5π/2
-4 ≤ 1/2 + n ≤ -5/2
-9/2 ≤ n ≤ -5/2
имеем целое значение n= -4 и корень π/2-4π= -5π/2
