How do you prove that $(1+tanx)/(sinx+cosx)=secx$ ?

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Answer 1 · 2015-02-14T18:26:29

You can use the followings:
$tan(x)=sin(x)/cos(x)$
$sec(x)=1/cos(x)$

Giving:

$(1+sin(x)/cos(x))/(sin(x)+cos(x))=1/cos(x)$

$(cos(x)+sin(x))/cos(x)*1/(sin(x)+cos(x))=1/cos(x)$

simplifying:

$1/cos(x)=1/cos(x)$

How do you prove that (1+tanx)/(sinx+cosx)=secx(1+tanx)/(sinx+cosx)=secx?