Стороны куба =a
по теореме косинусов
cos a=(A1O²+C1O²-A1C1²)/2A1O*C1O
A1C1²=a²+a²=2a²
A1C1=a√2
AO=a√2/2
A1O²=a²+(a√2/2)²=a²+2a²/4=3a²/2
A1O=C1O
cos a=(3a²/2+3a²/2-2a²)/2(a√6/2*a√6/2)=(2a²/2)/3a²=a²/3a³=1/3
2) DO²=DB²-OB²=1²-(1/2)²=3/4
DO=√3/2
AD=1
AO=√3/2
cos a=(AO²+DO²-AD²)/2AD*DO=((√3/2)²+(√3/2)²-1²))/2(√3/2*√3/2)=(1/2)/3/2)=1/3