[latex]a) (cos45^0-cos30^0)(cos45^0+cos30^0) = cos^245^0-cos^230^0 =\\ =(frac{sqrt2}{2})^2 -(frac{sqrt3}2)^2 = frac24-frac34 = -frac14\\\b) (3sin45^0+tg60^0)(3sin45^0-tg60^0) = 3^2sin^245^0-tg^260^0 = \\9(frac{sqrt2}2)^2-(sqrt3)^2 = 9*frac24-3 = 9*frac12-frac62 = frac{9-6}{2} = frac32 = 1frac12[/latex] [latex]c) (sin60^0+cos30^0)^2-(sin30^0+cos60^0)^2 = \\(frac{sqrt3}2+frac{sqrt3}2)^2-(frac12+frac12)^2 = (sqrt3)^2-1^2 = 3-1 = 2\\\d) 2(tg30^0-sin45^0)(cos45^0-ctg60^0) = \\2(frac{sqrt3}3-frac{sqrt2}2)(frac{sqrt2}2-frac{sqrt3}3) = -2*(frac{sqrt2}{2}-frac{sqrt3}{3})^2 = \\-2*((frac{sqrt2}{2})^2-2*frac{sqrt2}{2}*frac{sqrt3}{3}+(frac{sqrt3}3)^2) = \\-2*(frac{2}{4}-frac{sqrt6}{3}+frac39) = -1+frac{2sqrt6}{3}-frac69 = -1+frac{2sqrt6}{3}-frac23 = frac{2sqrt6-5}{3}[/latex]
