Question 1057128
.
prove this identity
1+ sin x/ cos x +cos x/ 1 + sin x = 2secx
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<pre>
{{{(1+ sin(x))/cos(x) +cos(x)/(1 + sin(x))}}} = {{{(1+sin(x))^2/(cos(x)*(1+sin(x))) + cos^2(x)/(cos(x)*(1+sin(x)))}}} = {{{((1+sin(x))^2 + cos^2(x))/(cos(x)*(1+sin(x)))}}} = 

{{{(1 + 2sin(x) + sin^2(x) + cos^2(x))/(cos(x)*(1+sin(x)))}}} =        ( <--- use {{{sin^2(x) + cos^2(x)}}} = 1 )

= {{{(2+2sin(x))/(cos(x)*(1+sin(x)))}}} =  {{{(2*(1+sin(x)))/(cos(x)*(1+sin(x)))}}} = {{{(2*cross((1+sin(x))))/(cos(x)*cross((1+sin(x))))}}} = {{{2/cos(x)}}} = 2*sec(x).


QED.
</pre>