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**A Beautiful Mind** Here is the problem:

$\displaystyle \frac{tan-cot}{tan+cot}+1 = 2sin^{2}$

I convert it into terms of cos and sin and try to simplify the left side.

$\displaystyle

\frac{sin}{cos}-\frac{cos}{sin}$

_________

$\displaystyle \frac{sin}{cos}+\frac{cos}{sin}$

Then, if I took it a step further and made them get a denominator of cos sin they'd end up on top with

$\displaystyle sin^{2}-cos^{2}$ and on the bottom $\displaystyle sin^{2}+cos^{2}$. I could make the bottom (using the Pythagorean identity):

$\displaystyle \frac{1}{cos sin}$

And that's how far I've gotten before everything fails.