Question

Por favor ajudem é urgente

Demonstre que:


a)$sen \: \alpha \times tg \: \alpha \: + \cos \: \alpha = sec \: \alpha$
b) Veja se:
senx • tgx = secx - cosx

Answer 1

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



$\sin( \beta ) \times \frac{ \sin( \beta ) }{ \cos( \beta ) } = \sec( \beta ) - \cos( \beta ) \\ \\ \frac{ \sin {}^{2} ( \beta ) }{ \cos( \beta ) } = \frac{1 - \cos {}^{2} ( \beta ) }{ \cos( \beta ) } = \frac{1}{ \cos( \beta ) } - \frac{ \cos {}^{2} ( \beta ) }{ \cos( \beta ) } \\ \\ = \sec( \beta ) - \cos( \beta )$