Question

Cos(x/2-pi/12)(sin(x-pi/3)+1)=0

Answer 1

1) cos(x/2-π/12)=0
x/2-π/12=π/2 + πk, k∈Z
x/2=π/12  + π/2 + πk
x/2= π/12 + 6π/12 + πk
x/2 = 7π/12 + πk
x= 2(7π/12 + πk)
x=7π/6 + 2πk, k∈Z

2) sin(x-π/3)+1=0
sin(x-π/3)= -1
x-π/3= -π/2 + 2πn, n∈Z
x=π/3 - π/2 + 2πn
x=2π/6 - 3π/6 + 2πn
x= - π/6 + 2πn, n∈Z

Ответ: 7π/6 + 2πk, k∈Z;
            - π/6 + 2πn, n∈Z