(secθ+tanθ)/(secθ-tanθ) is equal to:

$\frac{secθ+tanθ}{secθ-tanθ}$

= \(\frac{secθ+tanθ }{secθ-tanθ}\) × \(\frac{secθ+tanθ }{secθ+tanθ}\)

= \(\frac{ (secθ+tanθ)² }{sec²θ-tan²θ}\)

We know , sec²θ - tan²θ = 1

=  \(\frac{ (secθ+tanθ)² }{1}\)

= (secθ+tanθ)²