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 - c os2x) - 1 = 0;

-2cos2x + 1 = 0;

cos2x = 1/2;

2x = + -пи/3 + 2 пи * n,

x = + -пи/6 + пи*n, n - целое.