Question

упростите выражение, только 2

Answer 1

Ответ:

1

$\frac{ \sin( - \alpha ) \times ctg( \pi- \alpha ) }{ctg(360° - \alpha ) \times tg(\pi + \alpha) } = \\ = \frac{ - \sin( \alpha ) \times ( - ctg \alpha ) }{ - ctg \alpha \times tg \alpha } = \\ = - \sin( \alpha ) \times \frac{ \cos( \alpha ) }{ \sin( \alpha ) } = - \cos( \alpha )$

2

$\frac{ \sin(\pi + \alpha ) \times ctg(2\pi - \alpha ) }{ \cos(720° - \alpha ) \times tg(2\pi + \alpha )} = \\ = \frac{ - \sin( \alpha ) \times ( - ctg \alpha )}{ \cos( \alpha ) \times tg \alpha } = \\ = \frac{ \sin( \alpha ) \times \frac{ \cos( \alpha ) }{ \sin( \alpha ) } }{ \cos( \alpha ) \times \frac{ \sin( \alpha ) }{ \cos( \alpha ) } } = \frac{ \cos( \alpha ) }{ \sin( \alpha ) } = ctg( \alpha )$

3

$\frac{tg( - \alpha ) \times \cos(\pi - \alpha ) }{ \sin(\pi - \alpha ) \times ctg(\pi + \alpha )} = \\ = \frac{ - tg \alpha \times ( - \cos( \alpha )) }{ \sin( \alpha ) \times ctg \alpha } = \\ = \frac{ \sin( \alpha ) }{ \cos ( \alpha ) } = tg ( \alpha )$