Question

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

Answer 1

`x=kpi`

Explanation:

Since

`sin(alpha+-beta)=sinalpha cosbeta+-cosalpha sinbeta)`

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`