Question

преобразовать произведение в сумму sin(x+y)sin(x-y)

Answer 1

$\sin(x+y)\cdot\sin(x-y)=\\=\frac{1}{2}(\cos((x+y)-(x-y))-\cos((x+y)+(x-y)))=\\=\frac{1}{2}(\cos(x+y-x+y)-\cos(x+y+x-y))=\\=\frac{1}{2}(\cos2y-\cos2x)=\\=\frac{1}{2}(2\cos^2y-1-(2\cos^2x-1))=\\=\frac{1}{2}(2\cos^2y-1-2\cos^2x+1)=\\=\frac{1}{2}(2\cos^2y-2\cos^2x)=\\=\cos^2y-\cos^2x$