Question

Спростити вираз СРОЧНО

Answer 1

$\displaystyle\bf\\1)\\Cos64^\circ Cos34^\circ+Sin64^\circ Sin34^\circ=Cos(64^\circ-34^\circ)=Cos30^\circ=\frac{\sqrt{3} }{2} \\\\\\2)\\Sin(84^\circ-\alpha ) Cos(\alpha +24^\circ)-Cos(84^\circ-\alpha ) Sin(\alpha +24^\circ)=\\\\=Sin(84^\circ-\alpha -\alpha -24^\circ)=Sin(60^\circ-2\alpha )$

$\displaystyle\bf\\3)\\\\\frac{tg14^\circ+tg46^\circ }{1-tg14^\circ tg 46^\circ} =tg(14^\circ+46^\circ)=tg60^\circ=\sqrt{3} \\\\\\4)\\\\\frac{tg(\frac{\pi }{4} +\alpha )-tg\alpha }{1+tg(\frac{\pi }{4} +\alpha )tg\alpha } =tg\Big(\frac{\pi }{4} +\alpha -\alpha \Big)=tg\frac{\pi }{4} =1$