# How do you verify the identity 1/(csctheta+1)+1/(csctheta-1)=2sec^2thetasintheta?

$\frac{1}{\csc \theta + 1} + \frac{1}{\csc \theta - 1} = 2 {\sec}^{2} \theta \sin \theta$
$\frac{1}{\csc \theta + 1} + \frac{1}{\csc \theta - 1} = 2 \csc \frac{\theta}{{\csc}^{2} \theta - 1} =$
$= 2 \frac{{\sin}^{2} \theta \csc \theta}{\cos} ^ 2 \theta = 2 {\sin}^{2} \theta {\sec}^{2} \frac{\theta}{\sin} \theta = 2 \sin \theta {\sec}^{2} \theta$