Question

How do you verify the identity `cotalpha/(cscalpha+1)=(cscalpha-1)/cotalpha`?

Answer 1

Please see below.

Explanation:

`cotalpha/(cscalpha+1)`

= `cotalpha/(cscalpha+1)xxcotalpha/cotalpha`

= `cot^2alpha/(cotalpha(cscalpha+1))`

= `(csc^2alpha-1)/(cotalpha(cscalpha+1))`

= `((cscalpha-1)(cscalpha+1))/(cotalpha(cscalpha+1))`

= `(cscalpha-1)/cotalpha`