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Recall that: $\displaystyle \tan^2{x} = \sec^2{x} - 1$ Notice that $\displaystyle 1-\sec^2{x} = -(\sec^2{x}-1)$ You end up with $\displaystyle -\cot{x}\sin{x}$...Remember that $\displaystyle \cot{x} = \frac{\cos{x}}{\sin{x}}$
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