1. cos 4x cos x + sin 4x sin x =0
cos(4x-x) = 0
cos3x=0
3x= π/2+πn, n∈Z
x=π/6+πn/3, n∈Z
2. sin a =4/5=0,8, π/2<a<π. Найдите tg(π/4+a)
cos²a=1-0,8²
cos²a=0,36
cosa=-0,6
tga=sina/cosa
tga=0,8/(-0,6)=-4/3
tg(π/4+a) = (tgπ/4 + tga)/(1-tgatgπ/4)= (1-4/3)/(1+4/3) = (-1/3)/(7/3)= -1/7
1. cos 4x cos x + sin 4x sin x =0
cos(4x-x) = 0
cos3x=0
3x= π/2+πn, n∈Z
x=π/6+πn/3, n∈Z
2. sin a =4/5=0,8, π/2<a<π. Найдите tg(π/4+a)
cos²a=1-0,8²
cos²a=0,36
cosa=-0,6
tga=sina/cosa
tga=0,8/(-0,6)=-4/3
tg(π/4+a) = (tgπ/4 + tga)/(1-tgatgπ/4)= (1-4/3)/(1+4/3) = (-1/3)/(7/3)= -1/7