Question

упростить 1+2sina ×cosa/sina+cosa
$\frac{1 + 2 \sin( \alpha ) \times \cos( \alpha ) }{ \sin(\alpha ) + \cos( \alpha ) }$

Answer 1

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