Question

4sin210-3 корень из 2*cos(-135)

Answer 1

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