Sin α=4/5, π/2<α<π
cos α=α-√(1-16/25)=-3/5
tg α=sin α/cos α=-4/5*5/3=-4/3
sin 2α=2sinαcosα=2*4/5*(-3/5)=-24/25
С осью у при х=0: у=0+1=1, с осью х при у=0=-1.5х+1, 1.5х=1, х=2/3
…=5m(n+3)-10(n+3)=(n+3)(5m-10)
Вот. Простите за качество.
Sinx-cosx=1
2sin(x/2)cos(x/2)-cos²(x/2)+sin²(x/2)=sin²(x/2)+cos²(x/2)
2cos²(x/2)-2sin(x/2)cos(x/2)=0
cos(x/2)(cos(x/2)-sin(x/2))=0
cos(x/2)=0
x/2=π/2+πn
x=π+2πn
cos(x/2)-sin(x/2)=0
cos(x/2)=sin(x/2) I÷sin(x/2) sin(x/2)≠0 x≠2πn
ctg(x/2)=1
x/2=π/4+2πn x=5π/4+2πn
x=π/2+4πn x=5π/2+4πn
Ответ: х=π/2+2πn x=π+2πn.