Sin^2(x)+cos^2(2x)=1

$sin^{2x} +cos^{2} 2x=1$

$(1-cos2x) /2 + cos^22x=1$ домножим на 2

$1-cos2x +2 cos^2 2x=2$

$2 cos^2 2x -cos 2x -1=0$ заменим cos2x на y

$2 y^2 -y -1=0$

D = 9 ;

√D=+-3

y₁=-1/2 ;

cos2x = y₁= -1/2 ;

x =π*n - π/3, n ∈ Z

x =pi*n + pi/3, n ∈ Z

y₂= 1 ;

cos2x = y₂ =1 ;

x= π*n , n ∈ Z

Ответ: x =π*n - π/3, n ∈ Z ; x =π*n + π/3, n ∈ Z ; x= π*n , n ∈ Z