1. 4sin210°-3√2*cos(-135°)=4sin(180°+30°)-3√2cos(180°-45°)=
=4*(-sin30°)-3√2*(-cos 45°)=4*(-1/2)+3√2*(√2/2)=-2+3=1
2. 2ctg(5π/4)+√3tg(-5π/6)=2ctg(π+π/4)-√3tg(5π/6)=2ctgπ/4-√3tg(π-π/6)=2*1-√3*tg(π/6)=2-√3*(√3/3)=2-1=1
3. cos²(-5π/2+α)+cos²(8π-α)+2ctg(-3π/2+α)*ctg(5π-α)=
=cos²(5π/2-α)+cos²(8π-α)-2ctg(3π/2-α)*ctg(5π-α)=
=cos²(π/2-α)+cos²α-2tgα*(-ctgα)=sin²α+cos²α+21+2=3
4) А, В - больше 0, меньше 1, С - 1, D - 0
=-2cosa+(sina/tga+1)^2-cos^2a=-2cosa+(cosa+1)^2-cos^2a=-2cosa+cos^2a+2cosa+1-cos^2a=1
-cos(альфа+180)=cos альфа
-cos(aльфа+540)=cos альфа
-2sin(450-aльфа)=-2sin aльфа