Question

Решите с объяснением, пожалуйста)

Answer 1

$1)2Sin120^{o} -Ctg240^{o} +3Cos330^{o} =2Sin(180^{o}-60^{o})-Ctg(180^{o}+60^{o})+3Cos(360^{o}-30^{o} )=2Sin60^{o}-Ctg60^{0}+3Cos30^{o}=2*frac{sqrt{3} }{2}-frac{sqrt{3} }{3}+3*frac{sqrt{3} }{2}=frac{6sqrt{3} -2sqrt{3}+9sqrt{3}}{6} =frac{13sqrt{3} }{6}$

$2)Ctg105^{o}=Ctg(60^{o}+45^{o})=frac{Ctg60^{o}*Ctg45^{o} -1 } {Ctg60^{o}+Ctg45^{o}}=frac{frac{sqrt{3} }{3}*1-1 }{frac{sqrt{3} }{3}+1 } =frac{(sqrt{3}-3)*3 }{(sqrt{3}+3)*3 }=frac{sqrt{3}(1-sqrt{3} )}{sqrt{3}(1+sqrt{3})}=frac{1-sqrt{3} }{1+sqrt{3}}$

$3)Cosfrac{11pi }{10}Cosfrac{pi }{10}+Sinfrac{11pi }{10}Sinfrac{pi }{10}=Cos(frac{11pi }{10}-frac{pi }{10})= Cospi =-1$

$4)frac{tg24^{o} +tg6^{o} }{1-tg24^{0}tg6^{o}}=tg(24^{o}+6^{o})=tg30^{o} =frac{sqrt{3} }{3}$

$5)frac{Cos^{2}frac{pi }{5}+Sin^{2}frac{pi }{5}}{2Sinfrac{pi }{8}Cosfrac{pi }{8}}=frac{1}{Sinfrac{pi }{4} }=frac{1}{frac{1}{sqrt{2} } }=sqrt{2}$