Question 374918
<font face="Garamond" size="+2">


After struggling with this for 20 minutes, I finally let *[tex \Large x\ = \frac{\pi}{4}].


I'll leave it as an exercise for the student to verify that:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \cos\left(\frac{\pi}{4}\right)\sin^2\left(\frac{\pi}{4}\right)\ +\ \frac{\cos^3\left(\frac{\pi}{4}\right)}{\sin\left(\frac{\pi}{4}\right)}\ \neq\ \cot\left(\frac{\pi}{4}\right)].


which provides a counter example and proves that:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \cos\left(x\right)\sin^2\left(x\right)\ +\ \frac{\cos^3\left(x\right)}{\sin\left(x\right)}\ \not\equiv\ \cot\left(x\right)].





John
*[tex \LARGE e^{i\pi} + 1 = 0]
My calculator said it, I believe it, that settles it
<div style="text-align:center"><a href="http://outcampaign.org/" target="_blank"><img src="http://cdn.cloudfiles.mosso.com/c116811/scarlet_A.png" border="0" alt="The Out Campaign: Scarlet Letter of Atheism" width="143" height="122" /></a></div>
</font>