Question

Simplificar: Trigonométria 2

Answer 1

Recuerda:

$\cot(x) = \frac{1}{ \tan(x) }$

$\frac{ \frac{a}{b} }{ \frac{c}{d} } = \frac{a \times d}{b \times c}$

...

$E = \frac{ \tan( \alpha ) + \tan( \beta ) }{ \frac{1}{ \tan( \alpha ) } + \frac{1}{ \tan( \beta ) } } - \tan( \alpha ) \tan( \beta )$

$E = \frac{ \tan( \alpha ) + \tan( \beta ) }{ \frac{\tan( \alpha ) + \tan( \beta )}{\tan( \alpha ) \tan( \beta )} } - \tan( \alpha ) \tan( \beta )$

$E = \frac{(\tan( \alpha ) + \tan( \beta ) )\times \tan( \alpha ) \tan( \beta )}{\tan( \alpha ) + \tan( \beta )} - \tan( \alpha ) \tan( \beta )$

$E = \tan( \alpha ) \tan( \beta ) - \tan( \alpha ) \tan( \beta )$

$E = 0$