Question

Sin a Sin a
____ + _____
1+cos a 1-cos a

Answer 1

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

Answer 2

sina/(1+cosa)+sina/(1-cosa)=sina*(1-cosa+1+cosa)/(1-cos²a)=
=2sina/sin²a=2/sina