How do you multiply and simplify $(cosx+secx)^2$ ?

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Answer 1 · 2017-05-07T22:56:51

$cos^2x+2+sec^2x$

Expanding the binomial:

$(cosx+secx)^2=(cosx+secx)(cosx+secx)$

$=cos^2x+cosxsecx+cosxsecx+sec^2x$

Recall that $secx=1/cosx$ so $cosxsecx=cosx(1/cosx)=1$ :

$=cos^2x+2+sec^2x$

How do you multiply and simplify (cosx+secx)^2(cosx+secx)^2?