Sin(P/6 + x) - sin(P/6 -x)=1

Question

Sin(P/6 + x) - sin(P/6 -x)=1

Answer 1

sin(pi/6+x)-sin(p/6-x)=1

2sin((pi/6+x-pi/6+x))/2*cos((pi/6+x+pi/6-x))/2=1

2sin(x)*cos(pi/6)=1

2*sin(x)*(sqrt(3)/2)=1

sin(x)=1/sqrt(3)

x=(-1)^n*arcsin(1/sqrt(3)+pi*n