Question

ПОМОГИТЕ С ТЕСТОМ ПРЯМ СРОЧНО ДАЮ 18 БАЛЛОВ

Answer 1

Ответ:

а)

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

б)

$\frac{tg( \frac{3\pi}{2} + \alpha ) \times ctg(\pi + \alpha ) }{1 + {ctg}^{2} (\pi - \alpha )} = \frac{ - ctg \alpha \times ( - ctg \alpha ) }{1 + {ctg}^{2} \alpha } = \\ = {ctg}^{2} \alpha \times { \sin }^{2} \alpha = { \cos }^{2} \alpha$