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

[latex]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[/latex] Корней нет [latex]sin^2x=0\\ sin \ x=0\\ x=\pi\pm\pi n[/latex]