Question

$m = \sqrt{ 5} \: (sec \beta \: - \: \tan \beta )$

Teniendo en cuenta esto:
$si \: sen \: \beta = - \frac{1}{3} \: y \: \beta calcula \: el \: valor \: dea \: exprecion \: m$

Porfas ayúdenme que no entiendo nd ️️​

Answer 1

Explicación paso a paso:

$m = \sqrt{5} ( \sec( \beta ) - \tan( \beta ) )$

$m = \sqrt{5} ( \frac{1}{ \cos( \beta ) } - \frac{ \sin( \beta ) }{ \cos( \beta ) } ) \\ m = \sqrt{5} ( \frac{1 - \sin( \beta ) }{ \cos( \beta ) } )$

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

$m = \sqrt{5} ( \frac{1 - \sin( \beta ) }{ \sqrt{(1 - \sin {}^{2} ( \beta ) } } ) \\ m = \sqrt{5} ( \frac{1 - ( - \frac{1}{3} )}{ \sqrt{(1 - ( \frac{ - 1}{3} ) {}^{2} } } ) \\ m = \sqrt{5} ( \frac{(1 + \frac{1}{3} )}{ \sqrt{(1 + \frac{1}{9}) } } ) \\ m = \sqrt{5} ( \frac{ \frac{4}{3} }{ \sqrt{ \frac{10}{9} } } ) \\ m = \sqrt{5} ( \frac{ \frac{4}{3} }{ \frac{ \sqrt{10} }{3} } ) \\ m = \sqrt{5} ( \frac{4}{ \sqrt{10} } ) \\ m = \frac{4 \sqrt{5} }{ \sqrt{10} } = \frac{4 \sqrt{5} \times \sqrt{10} }{ \sqrt{10} \times \sqrt{10} } \\ m = \frac{4 \sqrt{50} }{10} = \frac{2 \sqrt{50} }{5}$