Question

Prove(sec theta-tan theta)(sec theta+tan theta)=1​

Answer 1

`( \sec \theta - \tan \theta)( \sec \theta + \tan \theta)`

from difference of two squares:

`{ \boxed{ \tt{( {a}^(2) - {b}^(2)) = (a - b)(a + b) }}}`

`= { \sec }^(2) \theta - { \tan}^(2) \theta \\ = (1 + { \tan}^(2) \theta) - { \tan}^(2) \theta \\ = 1`

hence proved