Question

cosa/1+sina + cosa/1-sina если соsa = -1/7

Answer 1

Ответ:

$\frac{ \cos( \alpha ) }{1 + \sin( \alpha ) } + \frac{ \cos( \alpha ) }{1 - \sin( \alpha ) } = \\ = \frac{ \cos( \alpha ) (1 - \sin( \alpha )) + \cos( \alpha )(1 + \sin( \alpha )) }{(1 + \sin( \alpha ))(1 - \sin( \alpha )) } = \\ = \frac{ \cos( \alpha ) (1 - \sin( \alpha ) + 1 + \sin( \alpha ) )}{1 - \sin {}^{2} ( \alpha ) } = \\ = \frac{ \cos( \alpha ) \times 2 }{ \cos {}^{2} ( \alpha ) } = \frac{2}{ \cos( \alpha ) } \\ \\ \frac{2}{ \cos( \alpha ) } = \frac{2}{ - \frac{1}{7} } = 2 \times ( - 7) = - 14$