Question

sinα__ _sinα
-------- + ---------
1+cosα 1-cosα

Answer 1

$frac{Sin alpha }{1+Cos alpha }+ frac{Sin alpha }{1-Cos alpha }= frac{Sin alpha -Sin alpha Cos alpha +Sin alpha +Sin alpha Cos alpha }{(1+Cos alpha )(1-Cos alpha )} = frac{2Sin alpha }{1-Cos ^{2} alpha } = frac{2Sin alpha }{Sin ^{2} alpha }$$= frac{2}{Sin alpha }$

Answer 2

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