SOLUTION: help verifying this identity please? sin (x + pi/6) - cos (x + pi/3) = sqrt of 3 sin x

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Question 916900: help verifying this identity please?
sin (x + pi/6) - cos (x + pi/3) = sqrt of 3 sin x

Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
sin (x + pi/6) - cos (x + pi/3) = sqrt of 3 sin x
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sin(x)*cos(pi/6) + cos(x)(sin(pi/6) - cos(x)cos(pi/3)-sin(x)sin(pi/3) = sqrt(3)sin(x)
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sin(x)(sqrt(3)/2))+ cos(x)(1/2) -[cos(x)(1/2)- sin(x)(sqrt(3)/2)] = sqrt(3)sin(x)
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2[sqrt(3)/2]sin(x) = sqrt(3)sin(x)
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sqrt(3)sin(x) = sqrt(3)sin(x)
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Cheers,
Stan H.