Question

How would you prove this?

Answer 1

see explanation

Explanation:

Using the trigonometric identities

tan²x + 1 = sec²x and sec x =
`(1)/(cosx)`

Consider the left side

Express the sum as a single fraction

`(secx+tanx+secx-tanx)/((secx-tanx)(secx+tanx))`

=
`(2secx)/(sec^2x-tan^2x)`

=
`(2secx)/(tan^2x+1-tan^2x)`

= 2sec x

=
`(2)/(cosx)` = right side ⇒ proven