prove that the left side is equal to the right side without using the right side
tan(t/2)*cos^2(t) - tan(t/2) =
tan(t/2)*(cos^2(t) - 1) =
[(1 - cos(t)) / sin(t)] * (-sin^2(t)) =
(1 - cos(t)) * (-sin(t)) = -sin(t) + (sin(t)*cos(t)) = (sin(t) / sec(t)) - sin(t).
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tan(t/2)*cos^2(t) - tan(t/2) =
tan(t/2)*(cos^2(t) - 1) =
[(1 - cos(t)) / sin(t)] * (-sin^2(t)) =
(1 - cos(t)) * (-sin(t)) = -sin(t) + (sin(t)*cos(t)) = (sin(t) / sec(t)) - sin(t).