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Explanation & Answer
sin(x+π/6)-sin(x-π/6)=1/2
sinA –Sin B=2cos[ (A+B)/2]*sin[(A-B)/2]
Putting the above equation in identity:
sin(x+π/6)-sin(x-π/6)=2cos[(x+π/6)+(x-π/6)/2]*sin[(x+π/6)-(x-π/6)/2]
=2cos(x)*sin(π/6)=1/2
=2*cos(x)*1/2=1/2
cos x=1/2
x=π/3 , 4π/3
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