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How do you prove $(sec (t) + 1) (sec (t) - 1) = {tan}^{2} (t)$ $(sec(t)+1)(sec(t)-1)=tan^2(t)$ ?

1 Answer

Mar 8, 2018

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Explanation:

$L H S : (sec t + 1) (sec t - 1)$ $LHS: (sect+1)(sect-1)$

$= {sec}^{2} t - 1$ $=sec^2t-1$ ->FOIL

$= {tan}^{2} t + 1 - 1$ $=tan^2t+1-1$ -> Use the property ${sec}^{2} t = {tan}^{2} t + 1$ $sec^2t=tan^2t+1$

$= {tan}^{2} t$ $=tan^2t$

$= R H S$ $=RHS$

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