Eliminate `theta "from the equation" m= tantheta +cottheta and n= tan theta - cot theta`.

Explanation

Given,
`m= tantheta +costheta" "(1)`
`n=tantheta-cottheta" "(2)`
Adding Eqs. (1) and (2), we get
`m+n= 2tantheta`
`m+n= 2tantheta`
`rArr tantheta = (m+n)/(2)`
Substracting Eq. (2) from Eq. (1), we get
`m-n= 2cottheta`
`rArrcostheta= (m-n)/(2)`
`therefore tan theta*cottheta=((m+n)/(2))*((m-n)/(2))`
`rArr tantheta*(1)/(tantheta)=(m^(2)-n^(2))/(4)`
`rArr1=(m^(2)-n^(2))/(4) orm^(2)-n^(2)=4`.
Hence, by eliminating '`theta`' we obtain the relation `m^(2)-n^(2)=4`.