Question

Sin^2(5x)=Sin4x+Sin^2(x)

Answer 1

$sin^2(5x)=sin(4x)+sin^2(x)<=>(sin(5x)-sin(x))(sin(5x)+sin(x))=\\=sin(4x)<=>4cos(3x)sin(2x)sin(3x)cos(2x)=sin(4x)<=>sin(4x)sin(6x)=\\=sin(4x)<=>sin(4x)(sin(6x)-1)=0\\sin(4x)=0=>x=\frac{\pi k}{4} \\sin(6x)=1=>x=\frac{\pi}{12}+\frac{\pi k}{3}$

k∈Z