Question

provar que 1+senx+icosx/1-senx-icosx=(tgx+senx)¡

Answer 1

$\frac{1+sinx+icosx}{1-sinx-icosx}$
$\frac{1+sinx+icosx}{1-sinx-icosx}\times\frac{1-sinx+icosx}{1-sinx+icosx}$
$\frac{1-sinx+icosx+sinx-sin^2x+isinxcosx+icosx-isinxcosx+i^2cos^2x}{1-sinx+icosx-sinx+sin^2x-isinxcosx-icosx+isinxcosx-i^2cos^2x}$
$\frac{1+2icosx-sin^2x+i^2cos^2x}{1-2sinx+sin^2x-i^2cos^2x}$
$\frac{cos^2x-cos^2x+2icosx}{1-2sinx+sin^2x+cos^2x}$
$\frac{2icosx}{1-2sinx+1}$
$\frac{2icosx}{2-2sinx}$
$\frac{icosx}{1-sinx}$
$\frac{icosx}{1-sinx}\times\frac{1+sinx}{1+sinx}$
$\frac{icosx(1+sinx)}{1-sin^2x}$
$\frac{icosx(1+sinx)}{cos^2x}$
$\frac{i(1+sinx)}{cosx}$
$i(secx+tanx)$