Question

Буду очень благодарна

Answer 1

$\frac{Cos\alpha-\sqrt{2}Cos(45^{0}+\alpha)}{2Sin(30^{0}+\alpha)-\sqrt{3}Sin\alpha }=\frac{Cos\alpha-\sqrt{2}(Cos45^{0} Cos\alpha-Sin45^{0} Sin\alpha)}{2(Sin30^{0} Cos\alpha+Cos30^{0} Sin\alpha)-\sqrt{3}Sin\alpha}=\\\\=\frac{Cos\alpha-\sqrt{2}(\frac{1}{\sqrt{2}}Cos\alpha-\frac{1}{\sqrt{2}}Sin\alpha) }{2(\frac{1}{2}Cos\alpha+\frac{\sqrt{3}}{2}Sin\alpha)-\sqrt{3}Sin\alpha}=\frac{Cos\alpha-Cos\alpha+Sin\alpha}{Cos\alpha+\sqrt{3}Sin\alpha-\sqrt{3}Sin\alpha}=$

$=\frac{Sin\alpha }{Cos\alpha }=\boxed{tg\alpha}$