Question

Упростить $frac{1+sin2 alpha}{sin alpha +cos alpha }$

Answer 1

$frac{1+sin2a}{sina+cosa}=frac{(sina+cosa)^2}{sina+cosa}=sina+cosa$ 
так как   $(sina+cosa)^2=sin^2+cos^2a+2sinacosa=1+sin2a$

Answer 2

$frac{1+sin2a}{sina+cosa}= \ \ frac{1+2sinacosa}{sina+cosa}= \ \ frac{sin^{2}a+cos^{2}a+2sinacosa}{sina+cosa}= \ \ frac{sin^{2}a+2sinacosa+cos^{2}a}{sina+cosa} \ \ (sin^{2}a+2sinacosa+cos^{2}a=(sina+cosa)^{2}) \ \ frac{(sina+cosa)^{2}}{sina+cosa}=sina+cosa$