Question

Помогите срочно алгебра 10 класс!!! Отдам все баллы!!! Все спамеры получат страйки даже не пытайтесь спамить!!!

Answer 1

Ответ:

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