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