№2
1а)=tg30=1/√3 б)=-ctgπ/3=-1/√3
2)=-sina*sina/tga*sina=-sina*cosa/sina=-cosa
3)=ctgπ/3=1/√3
4)=cos(47-17)=cos30=√3/2
5)=(sinacosb-cosasinb+2cosasinb)/(2cosacosb-cosacosb-sinasinb)=(sinacosb+cosasinb)/(cosacosb-siasinb)=sin(a+b)/cos(a+b)=tg(a+b)
6)=-sina*(-ctga)*tga/cosa+tga=tga*cta=1
7)sinπ/4cosa-cosπ/4sina=√2/2(cosa-sina)=√2/2(-√7/3-√2/3)=-√2/6(√7+√2)=(√14+2)/6
cosa=-√(1-2/9)=-√7/9=-√7/3
8)Sin179>0,tg175<0,cos410>0,cos(-116)<0<br>+*-/+*-=+
Выражение больше 0.
9)=(1+sin²a)ctg²a-(1+ctg²a)=(1+sin²a)cos²a/sin²a-1/sin²a=(cos²a+sin²acos²a-sin²a-cos²a)/sin²a=(sin²acos²a-sin²a)sin²a=sin²a(cos²a-1)/sin²a=cos²a-1=-sin²a
10)=√3cosa-2cosacosπ/6-2sinasinπ/6=√3cosa-√3cosa-sina=-sina
№3
1)=2sin45сos60=2*√2/2*1/2=√2/2
2)=(1-cosπ/6)/sinπ/6=(1-√3/2)/1/2=(2-√3)*2/2=2-√3
3)=1/2(cos(π/5-π/8)-cos(π/5+π/8))=1/2(cos3π/40-cos13π/40)
4)=(-cosa+sina)/(2cosa*(-sina)+1)=(sina-cosa)/(sin²a+cos²a-2sinacosa)=(sina-cosa)/(sina-cosa)²=1/(sina-cosa)
5)1+ctg²a=1/sin²a⇒sin²a=1:(1+1/25)=1:26/25=25/26
cos²a=1-sin²a=1-25/26=1/26
tg²a=sin²a/cos²a=25/26:1/26=25⇒tga=5 или tga=-5
tg2a=2tga/(1-tg²a)=2*5/(1-25)=-10/24=-5/12 или tg2a=5/12
6)=(cosπ/12+cosπ/4)+√3/2=2cos(π/12+π/4)/2*cos(π/12-π/4)/2+√3/2=2cosπ/6cosπ/12+√3/2=2*√3/2cosπ/12+√3/2=√3/2(2cosπ/12+1)
7)=√2(√2/2-cosa)=√2(cosπ/4-cosa)=√2(-2sin(π/8-a/2)sin(π/8+a/2))=-2√2sin(π/8-a/2)sin(π/8+a/2)
8)=2sinπ/2cosπ/9=2cosπ/9
Левая часть не равна правой, значит равенство неверно.
9)(cos²a/2-sin²a/2)(cos²a/2+sin²a/2)=(cos²a/2-sin²a/2)=cosa
10)=tg2a+3ctg2a=3
3=3