Задача 64950 ...
Условие
математика
1523
Решение
★
{sinx=2siny
{y=x-(5π/3)
{sinx=2sin(x-(5π/3))
Применяем формулу
[m]sin( α - β )[/m]
sinx=2*(sinx)*(cos(5π/3))-2*(cosx)*(sin(5π/3))
sinx=2*(sinx)*(1/2)-2*(cosx)*(sqrt(3)/2)
sinx=sinx-2(cosx)*(-sqrt(3)/2)
(sqrt(3))cosx=0
cosx=0
x=(π/2)+πk, k ∈ [b]Z[/b]
⇒
y=x-(5π/3)
y=(π/2)-(5π/3)+πk, k ∈ [b]Z[/b]
y=-(7π/6)+πk, k ∈ [b]Z[/b]
О т в е т. x=(π/2)+πk, k ∈ [b]Z[/b]; y=-(7π/6)+πk, k ∈ [b]Z[/b]