Question

sin^2(x)-sin^2(3x)=0

Answer 1

$sin^2x-sin^23x=0\ sin^2x-(3sin x-4sin^3x)^2=0\ sin^2x-(9sin^2x-12sin^4x+16sin^6x)=0\ sin^2x-9sin^2x+12sin^4x-16sin^6x=0\ -8sin^2x+12sin^4x-16sin^6x=0\ -2sin^2x+3sin^4x-4sin^6x=0\ t=sin^2x\ -2t+3t^2-4t^3=0\ -t(2-3t+4t^2)=0\ begin{cases} -t=0\ 4t^2-3t+2=0 end{cases}\ \ t_1=0;\ 4t^2-3t+2=0\ D=(-3)^2-4*4*2=-23 textless 0$
Корней нет
$sin^2x=0\ sin x=0\ x=pipmpi n$