α=π/8
sqrt(2)* (cos^2(π/8)-sin^2(π/8))=sqrt(2)cos(2*(π/8))=
=sqrt(2)*cos(π/4)=sqrt(2)*(sqrt(2)/2)=1
4.
1) α+β=0 - неверно, так как
-π/2 < α < 0
π < β < π/2
π/2 < α+β < π/2
2) cosα > 0
cos β < 0
cosα > cosβ - верно
3) -π/2 < α < 0
-π < - β < -π/2
Cкладываем:
-3π/2 < α - β < - π/2
α - β = 2 π - неверно
4) sinα =-sin β
sinα + sin β = 0 - верно
sqrt(2)*((cos(pi/8)^2)-(sin(pi/8)^2))=sqrt(2)* cos(pi/4)=sqrt(2)*(sqrt(2)/2)=2/2=1
4.
2 4