решите уравнение: sin(x+пи/3)cos(x-пи/6)=1
Ответ: пи/6 + пиn

1/2*sin(x+π/3-x+π/6)+1/2sin(x+π/3+x-π/6)=1
1/2sinπ/2+1/2*sin(2x+π/6)=1
1/2*sin(2x+π/6)=1/2
sin(2x+π/6)=1
2x+π/6=π/2+2πn,n∈z
2x=-π/6+π/2+2πn,n∈z
2x=π/3+2πn,n∈z
x=π/6+πn,n∈z