Question

1/secA+tanA=secA-tanA​

Answer 1

$\tt \blue{ \frac{1}{sec \theta + tan \theta} = sec \theta - tan \theta }$

$\tt \green{ \frac{1}{sec \theta \: + tan \theta} }$

$\tt \green{\frac{1}{sec \theta \: + tan \theta} \times \frac{sec \theta \: - tan \theta}{sec \theta \: - tan \theta} }$

$\tt \green{ \frac{sec \theta \: - tan \theta}{sec {}^{2} \theta - tan {}^{2} \theta } }$

We know that, 1+tan²=sec²

$\tt \green{ \frac{sec \theta \: - tan \theta}{1} }$

so..

$\tt \green{ \boxed{ \boxed{sec \theta - tan \theta}}}$

Hope my answer will help you.