Question

40 б. Упростить выражение (если можно с решением)

Answer 1

1)

$\sin( - \beta ) - \sin( \beta ) \cot( - \beta )^{2} = \\ = \sin( - \beta ) - \sin( \beta ) \cot( \beta )^{2} = \\ = \sin( - \beta ) - \frac{ \sin( \beta ) \cos( \beta )^{2}}{ { \sin( \beta ) }^{2} } = \\ = \sin( - \beta ) - \frac{ { \cos( \beta ) }^{2} }{ \sin( \beta ) } = \\ = - \frac{ { \sin( \beta ) }^{2} + \cos( \beta )^{2} }{ \sin( \beta ) } = \\ = - \frac{1}{ \sin( \beta ) }$

2)

$\cot(x) \tan( - x) + { \cos( - x) }^{2} = \\ = - ( \cot(x) \tan(x) ) + { \cos(x) }^{2} = \\ = - 1 + { \cos(x) }^{2} = \\ = - (1 - { \cos(x) }^{2} ) = - \sin(x)^{2}$