Question

sin a/1+cos a - sin a/1-cos a = - 2 ctg a​

Answer 1

Ответ:

$\dfrac{sina}{1+cosa}-\dfrac{sina}{1-cosa}=\dfrac{sina(1-cosa)-sina(1+cosa)}{(1+cosa)(1-cosa)}=\\\\\\=\dfrac{sina-sina\cdot cosa-sina-sina\cdot cosa}{(1+cosa)(1-cosa)}=\dfrac{-2sina\cdot cosa}{1-cos^2a}=\\\\\\=-\dfrac{2sina\cdot cosa}{sin^2a}=-\dfrac{2\cdot cosa}{sina}=-2\cdot ctga\\\\\\-2ctga=-2ctga$