# How do you determine if cot60^circ<cot75^circ is true or false?

Apr 21, 2018

It's false

#### Explanation:

Recall that $\frac{d}{\mathrm{dx}} \left(\cot x\right) = - {\csc}^{2} x$. If we convert to radians, we must prove whether or not

$\cot \left(\frac{\pi}{3}\right) < \cot \left(\frac{5 \pi}{12}\right)$

If you test within the derivative, you can see that at both these points the function is decreasing, and that since $- {\csc}^{2} x$ never equals $0$ in the interval $\left[\frac{\pi}{3} , \frac{5 \pi}{12}\right]$, cot(60˚) > cot(75˚)#, so the statement is false.

Hopefully this helps!