Question

sin(a-b)*sin(a+b)=(sina)^2 - (sinb)^2 уравнять

Answer 1

$\sin(a-b)\sin(a+b)=(\sin a\cos b-\sin b\cos a)(\sin a\cos b+\\+\sin b\cos a)=\sin^2a\cos^2b-\sin^2b\cos^2a=\\=\sin^2a(1-\sin^2b)-\sin^2b(1-\sin^2a)=\sin^2a-\sin^2a\sin^2b+\\+\sin^2b\sin^2a-\sin^2b=\sin^2a-\sin^2b\\ \boxed{\sin(a-b)\sin(a+b)=\sin^2a-\sin^2b}$