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

Question

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

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