Question 974152

(Sinx+tanx)(sinx÷1+cosx)=sinx×tanx prove the identity 
<pre>{{{(sin x + highlight(tan x))((sin x)/(1 + cos x)) = (sin x)(tan x)}}}
The left-side will be made equivalent to the right-side
{{{(sin x + highlight((sin x)/cos x))((sin x)/(1 + cos x)) = (sin x)(tan x)}}} --------- Converting tan x to {{{sin x/cos x}}}
{{{highlight(((cos x)(sin x) + sin x)/(cos x)) * ((sin x)/(1 + cos x)) = (sin x)(tan x)}}} ---- Multiplying by LCD, cos x
{{{highlight((sin x(cos x + 1))/(cos x)) * ((sin x)/(1 + cos x)) = (sin x)(tan x)}}} ---------- Factoring out GCF, sin x, in numerator
{{{highlight((sin x*cross((cos x + 1)))/(cos x)) * ((sin x)/cross((1 + cos x))) = (sin x)(tan x)}}} ------- Cancelling 1 + cos x in numerator and denominator
{{{((sin x)/(cos x)) * sin x = (sin x)(tan x)}}}, or {{{(sin x) * ((sin x)/(cos x)) = (sin x)(tan x)}}} 
{{{(sin x) * highlight(tan x) = (sin x)(tan x)}}} -------- Converting {{{(sin x)/(cos x)}}} to tan x
As seen, the left and right sides are congruent, hence the identity has been proven.