Question

How do you verify the identify `csctheta/cottheta=sectheta`?

Answer 1

See below.

Explanation:

Apply the following identities:

•`csctheta = 1/sintheta`

•`cottheta = 1/(tan theta) = 1/(sintheta/costheta) = costheta/sintheta`

•`sectheta = 1/costheta`

Now for the solution:

`(1/sintheta)/(costheta/sintheta) = 1/costheta`

`1/sintheta xx sintheta/costheta = 1/costheta`

`1/cancel(sintheta) xx cancel(sin theta)/costheta = 1/costheta`

`1/costheta = 1/costheta`

Identity proved!!

Hopefully this helps!