Verify the identity and explain how cot (x - pi/2) = - tan x

First, let's recall some usefull information:

- cot (x) = 1/tg (x) = cos (x) / sin (x)

- tan (x) = sin (x) / cos (x)

We also know that:

- cos (x - pi/2) = sin (x)

- sin (x - pi/2) = - cos (x)

Now we can use those relationships and get:

cot (x - pi/2) = cos (x - pi/2) / sin (x - pi/2) = sin (x) / -cos (x) = - tan (x)

So we have verified the identity, and explained step by step why the identity is true.