1)cos α=0,7 Найти 25 сos 2α
сos 2α=2cos²α-1
25 сos 2α=50(0,7 )²-1= 50·49/100 -1=49/2-2/2=47/2=23,5
2)3√2*sin 2п/8*cos 2п/8
3√2*sin 2п/8*cos 2п/8=3√2*sin п/4*cos п/4=3√2·(1/√2)·(1/√2)=3√2/2
или 3√2*(sin 2п/8*cos 2п/8)= 3√2*sin(2· 2п/8)/2=3√2*sin(п/2)/2=3√2/2
3)√12-√48*sin²17п/12
√12-√48*sin²17п/12=√12-√48*sin²(п+5п/12)=√12-√48*sin²(π/2-п/12)=
=√12-√48*cos²(п/12)=√12-√48*(1+cos2(п/12))/2=√12-√48*(1+cos(п/6))/2=
=√12-√48*(1+√3 /2)/2=√12-√12*(1+√3 /2))=√12(1-1-√3 /2)=2√3(-√3 /2)=-3
4)√200*cos²9п/8-√50
√200*cos²9п/8-√50=10√2·(1+cos(2·9п/8))/2-5√2=5√2·(1+cos(2·9п/8)-1)=
=5√2·cos(9п/4)=5√2·cos(2π+п/4)=5√2·cos(п/4)=5√2·√2 /2=5