Question

Find all solutions of the equation in the interval [0, 2pi). Show all work.

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

Answer 1

using the difference formula, you have

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

2cos(x)sin(π/6) = 1/2
2cos(x)(1/2) = 1/2
cos(x) = 1/2
x = π/3 or 5π/3

http://www.wolframalpha.com/input/?i=sin%28x%2B%28pi%2F6%29%29-sin%28x-%28pi%2F6%29%29%3D1%2F2+for+x+%3D+0+to+2pi