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