Eliminate `theta` from the equation `s=sin theta +"cosec" theta and r= sin theta-"cosec" theta` .

Explanation

Given, `s=sin theta + "cosec"theta" "`(1)
`r= sin theta- "cosec"theta" "`(2)
Adding Eqs. (1) and (2), we get
`s+r=2 sin theta `
`sin theta=(s+r)/(2)" " `(3)
Substrating Eq. (2) from Eq. (1), we get
`s-r=2 "cosec"theta`
`"cosec" theta=(s-r)/(2)" "` (4)
Multiplying Eqs. (3) and (4), we get
`sin theta * "cosec" theta=((s+r)/(2))((s-r)/(2))`
`sin theta*(1)/(sin theta)-(s^(2)-r^(2))/(4)`
`1=(s^(2)-r^(2))/(4) (or) s^(2)-r^(2)=4`.
Hence, by eliminating `theta`, we obtain the relation `s^(2)-r^(2)=4`.