Question

Simplify using trig identities: (sec θ + tan θ)(sec θ-tan θ)

Answer 1

$\bf \textit{Pythagorean Identities} \\\\ 1+tan^2(\theta)=sec^2(\theta)\implies 1=sec^2(\theta)-tan^2(\theta) \\\\[-0.35em] \rule{34em}{0.25pt}\\[0.8em] \stackrel{\textit{difference of squares}}{[sec(\theta )+tan(\theta )][sec(\theta )-tan(\theta )]}\implies [sec^2(\theta )-tan^2(\theta )]\implies 1$