sin^2 (x) + sin^2 (2x) = 1

Sin^2 x+sin^2 2x=1

sin^2 2x=1-sin^2 x

sin^2 2x=cos^2 x

4sin^2 x * cos^2 x=cos^2 x

cos^2 x * (4sin^2 x-1) = 0

1) cosx=0

x=пи/2+пи*n, n - целое

2) 4sin^2 x-1=0

2 (1-cos2x) - 1=0

-2cos2x+1=0

cos2x=1/2

2x=+-пи/3+2 пи*n,

x=+-пи/6+пи*n, n - целое

Ответ: x=пи/2+пи*n, x=+-пи/6+пи*n, n - целое