Question

Verify the identity.

cotx minus pi divided by two. = -tan x

Answer 1

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


hope it helps

Answer 2

Is an identity

Explanation:

If you need to verify an identity, you have to replace some values to x, like 30, 60, and if the both sides of the equation has the same result, they are an identity.

Then:

Remember that cotx=1/tanx

`cot((x-pi)/2)=1/[tan((x-pi)/2)]`

You can rewrite the original equation:

`1/[tan((x-pi)/2)]=-tanx`

Taking values for x and replacing:

x=30

`1/[tan((30-pi)/2)]=-tan30`

6,405=6,406; the same result in both sides

x=60

`1/[tan((60-pi)/2)]=-tan60`

-0,32=-0,32; the same result in both sides

It is an identity.