Question

докажите тождество 2/cosa- cosa/1+sina=1+sina/cosa

Answer 1

$frac{2}{cos alpha } - frac{cos alpha }{1+sin alpha }= frac{2+2sin alpha -cos^2 alpha }{cos alpha(1+sin alpha ) }=$
$frac{1+sin^2 alpha +cos^2 alpha +2sin alpha -cos^2 alpha }{cos alpha(1+sin alpha ) }=$
$frac{sin^2 alpha +2sin alpha +1 }{cos alpha(1+sin alpha ) }=$
$frac{(sin alpha +1)^2 }{cos alpha(1+sin alpha ) }=frac{sin alpha +1 }{cos alpha}$