How do you verify $(sec + tan)(sec - tan) = 1$ ?

Question

3843 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-07-15T06:16:30

$cos^2 alpha/cos^2 alpha=1$

Since

$(a+b)(a-b)=a^2-b^2$

you will have:

$(sec alpha+tan alpha)(sec alpha-tan alpha)=sec^2 alpha-tan^2 alpha$

then, since

$sec alpha=1/cos alpha$

and

$tan alpha=sin alpha/cos alpha$

you will have:

$1/cos^2 alpha-sin^2alpha/cos^2 alpha=$

$(1-sin^2 alpha)/cos^2 alpha=$

$cos^2 alpha/cos^2 alpha=1$

How do you verify (sec + tan)(sec - tan) = 1(sec + tan)(sec - tan) = 1?