5 sin(π/3+x)+7 sin(π/3-x)=0

Question

5 sin(π/3+x)+7 sin(π/3-x)=0

Answer 1

5sin(pi/3 + x) + 7sin(pi/3 - x) = 0
5sin(pi/3)*cos(x) + 5cos(pi/3)*sin(x) + 7sin(pi/3)*cos(x) - 7cos(pi/3)*sin(x) = 0
12sin(pi/3)*cos x - 2cos(pi/3)*sin x = 0
12*√3/2*cos x - 2*1/2*sin x = 0
6√3*cos x - sin x = 0
sin x = 6√3*cos x
tg x = 6√3
x = arctg(6√3) + pi*k