Question

4sin(2pix)*cos^2(2pix)+1+sin(4pix)+2cos(2pix)=0

Answer 1

$4sin(2pi x)cos^2(2pi x)+1+sin(4pi x)+2cos(2pi x)=0\\cos(2pi x)cdot (2sin(2pi x)cos(2pi x)+1)+(1+sin(4pi x))=0\\cos(2pi x)cdot (sin(4pi x)+1)+(1+sin(4pi x))=0\\(1+sin(4pi x))(cos(2pi x)+1)=0\\1); sin(4pi x)=-1,; 4pi x=-frac{pi}{2}+2pi n,; nin Z\\x=-frac{1}{8}+frac{n}{2},; nin Z\\2); cos(2pi x)=-1,; 2pi x=pi +2pi k,; kin Z\\x=frac{1}{2}+k,; kin Z$