# Cot x/ tan x × sec²x = cosec x how? prove it

May 10, 2018

We have;

$\frac{\cos \frac{x}{\sin} x}{\sin \frac{x}{\cos} x} \times \frac{1}{\cos} ^ 2 x = \frac{1}{\sin} x$

${\cos}^{2} \frac{x}{\sin} ^ 2 x \times \frac{1}{\cos} ^ 2 x = \frac{1}{\sin} x$

$\frac{1}{\sin} ^ 2 x = \frac{1}{\sin} x$

This is clearly FALSE so the identity cannot be proved. We can confirm graphically.

Since the two curves don't lie directly on each other, the given expression is an equation not an identity.

Hopefully this helps!