Question

If` (sec theta + tan theta)= m and ( sec theta - tan theta ) = n ,` show that mn =1

Answer 1

We have ` ( sec theta + tan theta ) =m                ....(i)`

Again ,` ( sec theta - tan theta ) = n                 .....(ii)`

Now, multiplying (i) and (ii), we get:

 `(sec theta + tan theta ) xx ( sec theta - tan theta ) = mn`

` => sec^2 theta - tan^2 theta = mn `

`= > 1= mn    [∵ sec^2 theta - tan^2 theta = 1 ]`

∴ mn = 1