Question

If `( cosec theta + cot theta ) =m and ( cosec theta - cot theta ) = n, ` show that mn = 1.

Answer 1

We have `(cosec  theta + cot theta ) = m      ............(i)`

Again ,`( cosec theta - cot theta )=n                 ............(ii)`

𝑁𝑜𝑤, 𝑚𝑢𝑙𝑡𝑖𝑝𝑙𝑦𝑖𝑛𝑔 (𝑖)𝑎𝑛𝑑 (𝑖𝑖), 𝑤𝑒 𝑔𝑒𝑡:

`(cosec theta + cot theta ) xx ( cosec theta - cot theta ) = mn`

= >`cosec  ^2 theta - cot^2  theta =mn`

= >1= mn     `[∵ cosec ^2 theta - cot^2 theta =1]`

∴  mn =1