Question

Помогите срочно пожалуйста, даю 50 баллов.

Answer 1

Ответ:

$\frac{ \cos {}^{2} ( \beta ) + 2}{ \cos {}^{2} ( \beta ) + 3\sin( \beta ) \cos( \beta ) } = \\ = \frac{ \cos {}^{2} ( \beta ) + 2 \sin {}^{2} ( \beta ) + 2\cos {}^{2} ( \beta ) }{ \cos {}^{2} ( \beta ) + 3\sin( \beta ) \cos( \beta ) } = \\ = \frac{3 \cos {}^{2} ( \beta ) + 2 \sin {}^{2} ( \beta ) }{ \cos {}^{2} ( \beta ) + 3\sin( \beta ) \cos( \beta ) } = \\ = \frac{ \cos {}^{2} ( \beta )(3 + \frac{2 \sin {}^{2} ( \beta ) }{ \cos {}^{2} ( \beta ) }) }{ \cos {}^{2} ( \beta ) (1 + \frac{3 \sin( \beta ) }{ \cos( \beta ) } )} = \frac{3 + 2tg {}^{2} \beta }{1 + 3tg \beta } = \\ \\ = \frac{3 + 2 \times 3}{1 + 3 \times3 } = \frac{3 + 6}{1 + 9} = \frac{9}{10} = 0.9$