How do you solve sin(x+pi/6)+sin(x-pi/6)=0sin(x+π6)+sin(xπ6)=0?

1 Answer
Jul 20, 2016

x=kpix=kπ

Explanation:

Since

sin(alpha+-beta)=sinalpha cosbeta+-cosalpha sinbeta)sin(α±β)=sinαcosβ±cosαsinβ)

you have the equivalent equation:

sinxcos(pi/6)+cancel(cosxsin(pi/6))+sinxcos(pi/6)-cancel(cosxsin(pi/6))=0

cancel2sinx*sqrt(3)/cancel2=0

sinx=0

x=kpi