How do you prove $tan(x) /( 1+tan(x)) = sin(x) /( sin(x)+cos(x))$ ?

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Answer 1 · 2016-04-23T02:51:27

Proof below

$tanx/(1+tanx)=tanx/(1+tanx) * cosx/cosx$
$=(sinx/cosx*cosx)/(cosx+sinx/cosx*cosx)$
$=sinx/(cosx+sinx)$
$=sinx/(sinx+cosx)$

How do you prove tan(x) /( 1+tan(x)) = sin(x) /( sin(x)+cos(x)) tan(x) /( 1+tan(x)) = sin(x) /( sin(x)+cos(x))?