# How do you verify the identity cotalpha/(cscalpha+1)=(cscalpha-1)/cotalpha?

Feb 6, 2017

#### Explanation:

$\cot \frac{\alpha}{\csc \alpha + 1}$

= $\cot \frac{\alpha}{\csc \alpha + 1} \times \cot \frac{\alpha}{\cot} \alpha$

= ${\cot}^{2} \frac{\alpha}{\cot \alpha \left(\csc \alpha + 1\right)}$

= $\frac{{\csc}^{2} \alpha - 1}{\cot \alpha \left(\csc \alpha + 1\right)}$

= $\frac{\left(\csc \alpha - 1\right) \left(\csc \alpha + 1\right)}{\cot \alpha \left(\csc \alpha + 1\right)}$

= $\frac{\csc \alpha - 1}{\cot} \alpha$