Question

Помогите решить тригонометрия ..............

Answer 1

$1)tg(\pi -\alpha )-2tg(-\alpha )=-tg\alpha +2tg\alpha=tg\alpha\\\\\alpha =-45^{o}\Rightarrow tg(-45^{o})=-tg45^{o}=-1\\\\2)Ctg(2\pi-\alpha)-2tg(-2\alpha)=-Ctg\alpha+2tg2\alpha\\\\\alpha=30^{o}\Rightarrow -Ctg30^{o} +2tg60^{o}=-\sqrt{3}+2\sqrt{3}=\sqrt{3}$

$3)Cos(3\pi -\alpha)-4Sin(-\alpha)=Cos(\pi-\alpha)+4Sin\alpha=-Cos\alpha+4Sin\alpha\\\\\alpha=-45^{o} \Rightarrow -Cos(-45^{o})+4Sin(-45^{o})=-\frac{\sqrt{2}}{2}-4*\frac{\sqrt{2}}{2}=-\frac{\sqrt{2}}{2}-2\sqrt{2}=-\frac{5\sqrt{2}}{2}\\\\4)Cos(3\pi-\alpha)-3Sin(-\alpha)=Cos(\pi-\alpha)+3Sin\alpha=-Cos\alpha+3Sin\alpha\\\\\alpha=-30^{o} \Rightarrow -Cos(-30^{o})+3Sin(-30^{o})=-\frac{\sqrt{3}}{2}-3*\frac{1}{2}=-\frac{\sqrt{3}}{2}-\frac{3}{2}=-\frac{\sqrt{3}+3}{2}$