8sin²x+4sin²2x=5-8cos2x

8sin^2 (x) + 4 (2sin (x) cos (x)) ^2=5-8 (cos^2 (x) - sin^2 (x))

8sin^2 (x) + 16sin^2 (x) cos^2 (x) = 5-8 ((1-sin^2 (x)) - sin^2 (x))

8sin^2 (x) + 16sin^2 (x) (1-sin^2 (x)) = 5-8 (1-2sin^2 (x))

8sin^2 (x) + 16sin^2 (x) - 16sin^4 (x) = 5-8+16sin^2 (x)

16sin^4 (x) - 8sin^2 (x) - 3=0

sin^2 (x) = t; 0<=t<=1

16t^2-8t-3=0

D = (2^3) ^2+2^2 * 2^4 * 3=2^6 (1+3) = 2^8

t = (8+-16) / 32

t=3/4

t=-1/4

0<=t<=1

t=3/4

sin^2 (x) = 3/4

(1-cos (2x)) / 2=3/4

1-cos (2x) = 3/2

cos (2x) = - 1/2

2x=-2 п/3 + 2 пk, k-целое число

2x=2 п/3 + 2 пn, n-целое число

х=-п/3 + пk

x=п/3 + пn

Ответ:-п/3 + пk; п/3 + пn