Question

решите уравнение cos7xsinx-sin7xcosx=0,5

Answer 1

cos7xsinx-sin7xcosx=0,5;
sin(x-7x)=1/2;
sin(-6x)=1/2;
-sin(6x)=1/2;
sin(6x)=-1/2;
6x=(-1)^k*arcsin(-1/2)+πk, k∈Z;
6x=(-1)^(k+1)*π/6+πk, k∈Z;
x=(-1)^(k+1)*∈π/36+πk/6, k∈Z.
Ответ: (-1)^(k+1)*∈π/36+πk/6, k∈Z.