Question

ПОМОГИТЕ ПОЖАЛУЙСТА ОЧ СРОЧНО 35 БАЛЛОВ

Answer 1

Ответ:

2.

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

4.

$\frac{ { \sin }^{2} (\alpha ) {tg}^{2} ( \alpha )}{ {tg}^{2} ( \alpha ) + { \cos }^{2} (\alpha ) - 1} = \frac{ { \sin }^{2} (\alpha ) {tg}^{2} ( \alpha ) }{ {tg}^{2} ( \alpha ) - (1 - { \cos }^{2} (\alpha ) )} = \\ = \frac{ { \sin }^{2}( \alpha ) {tg}^{2}( \alpha ) }{ {tg}^{2} ( \alpha ) - { \sin}^{2}( \alpha ) } = \frac{ { \sin }^{4} (\alpha )}{ { \cos}^{2}( \alpha ) } \times \frac{1}{ \frac{ { \sin}^{2}( \alpha ) }{ { \cos}^{2}( \alpha ) } - { \sin }^{2} (\alpha ) } = \\ = \frac{ { \sin}^{4} (\alpha )}{ { \cos }^{2} (\alpha ) } \times \frac{ { \cos}^{2}( \alpha )}{ { \sin}^{2} (\alpha )(1 - { \cos}^{2 }( \alpha )} = \frac{ { \sin }^{2} (\alpha )}{ { \sin}^{2} (\alpha )} = 1$