Verify the identity. cotangent of x divided by quantity one plus cosecant of x equals quantity cosecant of x minus one divided by cotangent of x

Step-by-step explanation:

We want to verify the identity:

Let us take the LHS and simplify to get the LHS.

Express everything in terms of the cosine and sine function.

Collect LCM

We simplify the RHS to get:

We rationalize to get:

We expand to get:

Factor negative one in the denominator:

Apply the Pythagoras Property to get:

Simplify to get:

Or

Divide both the numerator and denominator by sin x

This finally gives: