Question

How do you verify the identify `cotthetasectheta=csctheta`?

Answer 1

The following identities are very important:

•`tanalpha = sin alpha/cosalpha`

•`cscalpha = 1/sinalpha`

•`secalpha = 1/cosalpha`

•`cotalpha = 1/tanalpha`

Applying the aforementioned identities:

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

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

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

`1/sintheta = 1/sintheta`

Identity proved!!

Hopefully this helps!