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Verify the identity cot(x-pi/2)=-tanx

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\cot(x-(\pi)/(2)) = (\cos(x-(\pi)/(2)))/(\sin(x-(\pi)/(2))) =(\cos(-((\pi)/(2)-x)))/(\sin(-((\pi)/(2)-x))) =(\cos((\pi)/(2)-x))/(-\sin((\pi)/(2)-x)) =\\=-(\sin x)/(\cos x) = -\tan x
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