# How do you prove costhetacottheta=costheta?

Consider $\theta = \frac{\pi}{3}$. Then $\cos \left(\theta\right) = \frac{1}{2}$, and $\cot \left(\theta\right) = \cos \frac{\theta}{\sin} \left(\theta\right) = \frac{\frac{1}{2}}{\frac{\sqrt{3}}{2}} = \frac{\sqrt{3}}{3}$
So $\cos \left(\theta\right) \cot \left(\theta\right) = \frac{1}{2} \left(\frac{\sqrt{3}}{3}\right) = \frac{\sqrt{3}}{6} \ne \frac{1}{2} = \cos \left(\theta\right)$