Question

sin^2 x + cos^2 2x = 1

Answer 1

$sin^2x+cos^22x=1;\ sin^2x+(cos2x)^2=1;\ sin^2x+(1-2sin^2x)^2=1;\ 4sin^4x-4sin^2x+1+sin^2x=1;\ 4sin^4x-3sin^2x=0;\ sin^2x(4sin^2x-3)=0;\ 1)sin^2x=0;\ sin x=0;\ x=pi n, nin Z;\ 2)4sin^2x-3=0;\ sin^2x=frac34;\ sin x=pmfrac{3}{2};$
$a) sin x=+frac{sqrt3}{2};\ x=(-1)^karcsinfrac{sqrt3}{2}+pi k\ x=(-1)^kfracpi3+pi k;\ b)sin x=frac{sqrt3}{2};\ x=(-1)^marcsin(-frac{sqrt3}{2})+pi m;\ x=-(-1)^marcsinfrac{sqrt3}{2}+pi m;\ x=-(-1)^mfracpi3+pi m;\ a)bigcup b): x=pm(-1)^kcdotfrac{pi}{3}+pi k, kin Z;\ \ \ \ left[ {{x=pi n, } atop {x=-(-1)^kcdotfrac{pi}{3}+pi k}} right. n,kin Z$