Упростите выражение sina/1+cosa+1+cosa/sina=2/sina

[latex] \frac{sin \alpha }{1+co \alpha } + \frac{1+cos \alpha }{sin \alpha } = \frac{sin ^{2} \alpha +(1+cos \alpha ) ^{2} }{(1+cos \alpha )sin \alpha } = \frac{sin ^{2} \alpha +1+2cos \alpha +cos ^{2} \alpha }{(1+cos \alpha )sin \alpha} =[/latex] [latex] =\frac{2+2cos \alpha }{(1+cos \alpha )sin \alpha} =\frac{2(1+cos \alpha ) }{(1+cos \alpha )sin \alpha}= \frac{2}{sin \alpha } [/latex]