Question

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

Answer 1

$sin(a-b)sin(a+b)=(sin acos b-sin bcos a)(sin acos b+\+sin bcos a)=sin^2acos^2b-sin^2bcos^2a=\=sin^2a(1-sin^2b)-sin^2b(1-sin^2a)=sin^2a-sin^2asin^2b+\+sin^2bsin^2a-sin^2b=sin^2a-sin^2b\ boxed{sin(a-b)sin(a+b)=sin^2a-sin^2b}$