Question

((sin a)/(1 + cos alpha) + (sin alpha)/(1 - cos alpha)) * sin 2alpha underline​

Answer 1

Ответ:

$\boxed{ \sin 2\alpha \bigg (\dfrac{\sin \alpha }{1 + \cos \alpha } + \dfrac{\sin \alpha }{1 - \cos \alpha } \bigg ) = 4 \cos \alpha }$

Объяснение:

$\sin 2\alpha \bigg (\dfrac{\sin \alpha }{1 + \cos \alpha } + \dfrac{\sin \alpha }{1 - \cos \alpha } \bigg ) = \sin 2\alpha \bigg (\dfrac{\sin \alpha (1 - \cos \alpha ) + \sin \alpha (1 + \cos \alpha }{(1 + \cos \alpha )(1 - \cos \alpha )} \bigg)=$

$= \sin 2\alpha \bigg (\dfrac{\sin \alpha - \sin \alpha \cos \alpha + \sin \alpha+ \sin \alpha \cos \alpha }{1 - \cos^{2} \alpha } \bigg)= \sin 2\alpha \bigg (\dfrac{2\sin \alpha }{\sin^{2} \alpha } \bigg)=$

$= \dfrac{2 \sin 2\alpha }{\sin \alpha } = \dfrac{2 \cdot 2\sin \alpha \cos \alpha }{\sin \alpha } = 4 \cos \alpha$