Please show work, thanks in advance!
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sin(t - pi/6) =>
sin(t)cos(pi/6) - sin(pi/6)cos(t) =>
sin(t) * (sqrt(3)/2) - (1/2) * cos(t) =>
(1/2) * (sqrt(3) * sin(t) - cos(t)) =>
(1/2) * (sqrt(3) * (-sqrt(1 - cos(t)^2)) - cos(t))
Without knowing the value of cos(t), this is the best that can be done.
sin(t)cos(pi/6) - sin(pi/6)cos(t) =>
sin(t) * (sqrt(3)/2) - (1/2) * cos(t) =>
(1/2) * (sqrt(3) * sin(t) - cos(t)) =>
(1/2) * (sqrt(3) * (-sqrt(1 - cos(t)^2)) - cos(t))
Without knowing the value of cos(t), this is the best that can be done.