(Cotanx +cosecx)(cotanx-cosecx)

[tex]$\begin{align} (cotan~x + cosec~x)(cotan~x-cosec~x) &= cotan^2x - cosec^2x \\ &= \frac{cos^2x}{sin^2x} - \frac{1}{sin^2x} \\ &= \frac{cos^2x - 1}{sin^2x} \\ &= \frac{(1 -sin^2x) - 1}{sin^x} \\ &= \frac{-sin^2x}{sin^2x} \\ &= -1 \end{align}[/tex]