Respuesta:
[tex] \frac{tan( \alpha ) \times \cos( \alpha ) }{ \cos( \alpha ) \times \sin( \alpha ) } = \frac{ \tan( \alpha ) }{ \sin( \alpha ) } = \frac{ \frac{ \sin( \alpha ) }{ \cos( \beta ) } }{ \sin( \alpha ) } \\ \frac{ \sin( \alpha ) }{ \cos( \alpha ) \times \sin( \alpha ) } = \frac{1}{ \cos( \alpha ) } [/tex]
[tex] \sec( \alpha ) \times \csc( \alpha ) = \frac{1}{ \cos( \alpha ) } \times \frac{1}{ \sin( \alpha ) } = \frac{1}{ \cos( \alpha ) \times \sin( \alpha ) } [/tex]
[tex]{ \sin}^{2} ( \alpha ) + { \cos}^{2} ( \alpha ) - 1 \\ 1 - 1 = 0[/tex]
[tex] \sec( \alpha ) ( \csc( \alpha ) + 1) \\ \frac{1}{ \cos( \alpha ) } ( \frac{1}{ \sin( \alpha ) + 1 } ) \\ \frac{1}{ \cos( \alpha ) } ( \frac{1 + \sin( \alpha ) }{ \sin( \alpha ) } ) \\ \frac{1 + \sin( \alpha ) }{ \cos( \alpha) \times \sin( \alpha ) } [/tex]
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Verified answer
Respuesta:
[tex] \frac{tan( \alpha ) \times \cos( \alpha ) }{ \cos( \alpha ) \times \sin( \alpha ) } = \frac{ \tan( \alpha ) }{ \sin( \alpha ) } = \frac{ \frac{ \sin( \alpha ) }{ \cos( \beta ) } }{ \sin( \alpha ) } \\ \frac{ \sin( \alpha ) }{ \cos( \alpha ) \times \sin( \alpha ) } = \frac{1}{ \cos( \alpha ) } [/tex]
[tex] \sec( \alpha ) \times \csc( \alpha ) = \frac{1}{ \cos( \alpha ) } \times \frac{1}{ \sin( \alpha ) } = \frac{1}{ \cos( \alpha ) \times \sin( \alpha ) } [/tex]
[tex]{ \sin}^{2} ( \alpha ) + { \cos}^{2} ( \alpha ) - 1 \\ 1 - 1 = 0[/tex]
[tex] \sec( \alpha ) ( \csc( \alpha ) + 1) \\ \frac{1}{ \cos( \alpha ) } ( \frac{1}{ \sin( \alpha ) + 1 } ) \\ \frac{1}{ \cos( \alpha ) } ( \frac{1 + \sin( \alpha ) }{ \sin( \alpha ) } ) \\ \frac{1 + \sin( \alpha ) }{ \cos( \alpha) \times \sin( \alpha ) } [/tex]