# Thread: Verify that this is an identity.

1. ## Verify that this is an identity.

1. (tan u - cot u) / (tan u + cot u) is an identity.

(tan u - cot u) / (tan u + cot u)
= [(sin u/cos u) - (cos u/sin u)] / [(sin u/cos u) + (cos u/sin u)]
= (sinē u - cosē u) / (sinē u + cosē u)
= sinē u - cosē u

is there any other mid steps that would be good to include?

2. ## Re: Verify that this is an identity.

Originally Posted by JamesBond16
1. (tan u - cot u) / (tan u + cot u) is an identity.

(tan u - cot u) / (tan u + cot u)
= [(sin u/cos u) - (cos u/sin u)] / [(sin u/cos u) + (cos u/sin u)]
This is a BIG jump. You might want to break down the steps.
= (sinē u - cosē u) / (sinē u + cosē u)
= sinē u - cosē u

is there any other mid steps that would be good to include?

3. ## Re: Verify that this is an identity.

Hello, JamesBond16!

(tan u - cot u) / (tan u + cot u) is not an identity.

4. ## Re: Verify that this is an identity.

Originally Posted by Soroban
Hello, JamesBond16!

(tan u - cot u) / (tan u + cot u) is not an identity.
Of course you're right, but it looks like JamesBond16 was proving the identity:

(tan u - cot u) / (tan u + cot u) = sinē u - cosē u .