Question

Prove the identity, note that each statement must be based on a Rule.

Answer 1

see explanation

Explanation:

using the identity

tan²x + 1 = sec²x ( subtract 1 from both sides )

tan²x = sec²x - 1 ← factor as a difference of squares

tan²x = (secx - 1)(secx + 1)

consider left side

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

=
`((secx-1)(secx+1))/(secx-1)` ← cancel (secx - 1) on numerator/ denominator

= secx + 1

= right side , hence proven