# How do you prove Cot^2 (theta) + 5 = 6 Cot (theta)?

Jun 19, 2016

Impossible.

#### Explanation:

It is impossible. Take an example to prove it:
$t = \frac{\pi}{3}$ --> $\cot \left(\frac{\pi}{3}\right) = \frac{\sqrt{3}}{3}$ --> ${\cot}^{2} \left(\frac{\pi}{3}\right) = \frac{3}{9} = \frac{1}{3}$
$\frac{1}{3} + 5$ different to $6 \left(\frac{\sqrt{3}}{3}\right)$
However, the equation is true when $t = \frac{\pi}{4} + 2 k \pi$
$t = \frac{\pi}{4}$ --> cot t = 1 --> ${\cot}^{2} t = 1$-->
1 + 5 = 6(1). OK