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$\begingroup$

$$\tan\left(\frac{\pi}{2} -x\right) - \cot\left(\frac{3\pi}{2} -x\right) + \tan(2\pi-x) - \cot(\pi-x) = \frac{4-2\sec^{2}x}{\tan{x}}$$

L.S.

$= \cot{x} - \tan{x} - \tan{x} + \cot{x}$

$= 2\cot{x} - 2\tan{x}$

$= 2\left(\frac{\cos{x}}{\sin{x}} - \frac{\sin{x}}{\cos{x}}\right)$

$= 2\left(\frac{\cos^{2}x - \sin^{2}x}{\sin{x}\cos{x}}\right)$

$= 2\left(\frac{1-2\sin^{2}x}{\sin{x}\cos{x}}\right)$

$= \frac{4 - 2\sin^{2}x}{\sin{x}\cos{x}}$

  • Not sure where to go from here.
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    You may want to look here (http://meta.math.stackexchange.com/questions/5020/mathjax-basic-tutorial-and-quick-reference) on how to typeset your questions so that it is easier for people to read.2012-11-08

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