# How do you verify the identity tanx+cotx=2csc2x?

##### 1 Answer
May 25, 2015

$\sin \frac{x}{\cos} x + \cos \frac{x}{\sin} x$ = $\frac{{\sin}^{2} x + {\cos}^{2} x}{\sin x . \cos x}$ =

$= \frac{1}{\sin x . \cos x} = \frac{1}{\left(\frac{1}{2}\right) \left(\sin 2 x\right)} = \frac{2}{\sin 2 x} = 2 \csc 2 x .$