Question

What identity is this? If it would be pythagorean identity the identity would change from csc squared to cot squared plus one

Answer 1

`1+cot^2x=csc^2x`

Explanation:

You have described the following Pythagorean identity relating the cosecant and cotangent:

`1+cot^2x=csc^2x`

Answer 2

Pythagorean Identity

Explanation:

`csc^2theta= cot^2theta+1`

You can either state this is a pythagorean identity, or you can turn it into the any other pythagorean identity, for example: `sin^2theta+cos^2theta=1`

`csc^2theta= cot^2theta+1`

Multiply the given expression by `sin^2theta`

`sin^2theta(csc^2theta)= sin^2theta(cot^2theta+1)`

Apply reciprocal identity and quotient identity: `csctheta=1/sintheta` and `cottheta=costheta/sintheta`

`cancel(sin^2theta)(1/cancel(sin^2theta))= cancel(sin^2theta)*cos^2theta/cancel(sin^2theta)+1*sin^2theta`

`1= cos^2theta+sin^2theta`

Which is a pythagorean identity as well