How do you solve sin(x+pi/6)+sin(x-pi/6)=0sin(x+π6)+sin(x−π6)=0? Trigonometry Trigonometric Identities and Equations Sum and Difference Identities 1 Answer Gerardina C. 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 Answer link Related questions What are some sum and difference identities examples? How do you use the sum and difference identities to find the exact value of cos 15^@? How do you use the sum and difference identities to find the exact value of cos 75? How do you use the sum and difference identities to find the exact value of tan 105 degrees? How do you apply the sum and difference formula to solve trigonometric equations? How do you evaluate sin(45)cos(15)+cos(45)sin(15)? How do you write cos75cos35+sin75sin 35 as a single trigonometric function? How do you prove that cos(x-y) = cosxcosy + sinxsiny? How do you evaluate cos((3pi)/5)cos((4pi)/15)+sin((3pi)/5)sin((4pi)/15)? If sinA=4/5 and cosB= -5/13, where A belongs to QI and B belongs to QIII, then find sin(A+B).... See all questions in Sum and Difference Identities Impact of this question 3757 views around the world You can reuse this answer Creative Commons License