Question

How do you verify the identity `(csc^2theta+2csctheta-3)/(csc^2theta-1)=(csctheta+3)/(csctheta+1)`?

Answer 1

`LHS=RHS`

Explanation:

`LHS`
`=(csc^2 theta+2csc theta-3)/(csc^2 theta-1)`
`=(csc^2 theta-csc theta+3csc theta-3)/((csc theta-1)(csc theta+1))`
`=(csc theta(csc theta-1)+3(csc theta-1))/((csc theta-1)(csc theta+1)`
`=(cancel((csctheta-1))(csc theta+3))/((cancel(csc theta-1))(csc theta+1)`
`=(csc theta+3)/(csc theta+1`
Hence
`LHS=RHS`