Question

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

Answer 1

$1)tg(pi -alpha )-2tg(-alpha )=-tgalpha +2tgalpha=tgalpha\\alpha =-45^{o}Rightarrow tg(-45^{o})=-tg45^{o}=-1\\2)Ctg(2pi-alpha)-2tg(-2alpha)=-Ctgalpha+2tg2alpha\\alpha=30^{o}Rightarrow -Ctg30^{o} +2tg60^{o}=-sqrt{3}+2sqrt{3}=sqrt{3}$

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