Verified answer

Ответ:

[tex]\boxed{ \sin 2\alpha \bigg (\dfrac{\sin \alpha }{1 + \cos \alpha } + \dfrac{\sin \alpha }{1 - \cos \alpha } \bigg ) = 4 \cos \alpha }[/tex]

Объяснение:

[tex]\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)=[/tex]

[tex]= \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)=[/tex]

[tex]= \dfrac{2 \sin 2\alpha }{\sin \alpha } = \dfrac{2 \cdot 2\sin \alpha \cos \alpha }{\sin \alpha } = 4 \cos \alpha[/tex]