[latex]a) 2sin 30^o+tg45^o+3cos60^o = 2*frac12+1+3*frac12 = 1+1+1frac12 = 3frac12\\b) tg30^0*ctg60^o-ctg45^o = frac{sqrt3}3*frac{sqrt3}{3} - 1 =frac13-1 = -frac23\\c) sin60^o*cos30^o+sin45^o*cos45^o = frac{sqrt3}{2}*frac{sqrt3}{2}+(frac{sqrt2}{2})^2 = \\frac34+frac24 = frac54= 1frac14\\e) ctg45^o*cos60^o-sin60^o*tg60^o = 1*frac12-frac{sqrt3}{2}*sqrt3 = frac12-frac32 = -1\\f) 4ctg^230^o-tg^230^o = 4*(sqrt3)^2-(frac{sqrt3}3)^2 = 4*3-frac39 = 12-frac13 = 11frac23[/latex]
[latex]a) 2sin30^{o}+tg45^{o}+3cos60^{o}= 2*frac{1}{2}+1+3*frac{1}{2}=\ =1+1+frac{3}{2}= 2frac{3}{2}=3frac{1}{2}\ \ b) tg30^{o}*ctg60^{o}-ctg45^{o}= frac{sqrt{3}}{3}*frac{sqrt{3}}{3}-1= frac{3}{9}-1= frac{1}{3}-1=-frac{2}{3}\ \ c) sin60^{o}*cos30^{o}+sin45^{o}*cos45^{o}= frac{sqrt{3}}{2}*frac{sqrt{3}}{2}+frac{sqrt{2}}{2}*frac{sqrt{2}}{2}=\ =frac{3}{4}+frac{2}{4}=frac{5}{4}=1frac{1}{4} [/latex] [latex]e) ctg45^{o}*cos60^{o}-sin60^{o}*tg60^{o}= 1*frac{1}{2}-frac{sqrt{3}}{2}*sqrt{3}=\ =frac{1}{2}-frac{3}{2}=-frac{2}{2}=-1\ \ f) 4ctg^{2}30^{o}-tg^{2}30^{o}= 4*sqrt{3}^{2}-frac{sqrt{3}}{3}= 4*3-frac{3}{9}= 12-frac{1}{3}=11frac{2}{3}[/latex]