# Verify that this is an identity.

• Jul 24th 2011, 01:52 PM
JamesBond16
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?
• Jul 26th 2011, 07:43 PM
SammyS
Re: Verify that this is an identity.
Quote:

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.
Quote:

= (sinē u - cosē u) / (sinē u + cosē u)
= sinē u - cosē u

is there any other mid steps that would be good to include?
• Jul 26th 2011, 08:23 PM
Soroban
Re: Verify that this is an identity.
Hello, JamesBond16!

(tan u - cot u) / (tan u + cot u) is not an identity.
• Jul 27th 2011, 09:14 AM
SammyS
Re: Verify that this is an identity.
Quote:

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 .