Question

Ребят, помогите решить, срочно нужно:

Answer 1

$\\\sin\alpha\cos\beta-\sin\beta\cos\alpha=\sin(\alpha-\beta)\\\cos\alpha\cos\beta-\sin\alpha\sin\beta=\cos(\alpha+\beta)\\\frac{\sin72^o\cos12^o-\sin12^o\cos72^o}{\cos18^o\cos12^o-\sin18^o\sin18^o}=\frac{\sin(72^o-12^o)}{\cos(18^o+12^o)}=\frac{\sin60^o}{\cos30^o}=\frac{\frac1{\sqrt2}}{\frac1{\sqrt2}}=1$