Question

упростить выражение. sin(a+b)-sin(a-b)

Answer 1

$Sin(\alpha+\beta)-Sin(\alpha-\beta)= 2Sin\frac{\alpha+\beta-\alpha+\beta}{2}Cos\frac{\alpha+\beta+\alpha-\beta}{2}=\boxed{2Sin\beta Cos\alpha}$

Answer 2

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